CURRICULUM VITAE
JAMES A.
YORKE
December 2011
Chair of Mathematics
Distinguished
University Professor of Mathematics and
Web page: http://yorke.umd.edu
e-mail: yorke at umd.edu
phone: 301-405-5051
Born
1941 in
Education
University of
Professional Positions
Appointments in the IPST (“IPST” denotes the Institute for Physical Science and Technology or in its predecessors, at the University of Maryland). JY has held joint appointments with Mathematics since 1976 and Physics since 2000.
Research Associate, 1966-1967
Research Assistant Professor
1967-1969
Research Associate Professor
1969-1973
Professor 1973-present
Director of IPST (Acting
Director 1985-1988) 1988-Dec 2001
Distinguished University
Professor since 1995
Director
of Applied Math. and Scientific Computing (
graduate program 2006-2007
Chair of Mathematics, 2007- (a five year appointment)
Expert (part-time appointment) National Cancer Institute 1978-1979
Honors and Awards
Jurgen Moser lecture/award 2011 presented in Snowbird Utah
Norbert Wiener Lecturer – Tufts University Fall 2006
Commencement address May 2006 University School of Health Information Sciences
Penn State University 2006 Marker Lecturer in Mathematics
Fellow of the American Physical Society, appointed 2003
Japan Prize Laureate 2003 (shared with Benoit Mandelbrot); see www.japanprize.jp The Japan Prize for Science and Technology is a Japanese version of the Nobel Prize. One is awarded in medical science and one in the rest of science and technology. The Emperor of Japan presides over the awards ceremony.
Distinguished Alumnus Award 2002, alumnus of U of Md. College of Computer Math, and Physics Sciences.
An
AAAS Fellow - elected 1998
First UMCP
recipient of the
38th Annual Chaim
Weizmann Memorial Lecturer
- Weizmann Institute Rehovot,
Distinguished University Professor - appointed 1995
Guggenheim fellow 1980
Principal investigator on current research
grants
NSF
grants 2001-2010 Applications of Nonlinear Dynamics
NIH grant 2003-10 Reliable Assembler for Whole Genome Shotgun Data
Editorial boards
International Journal of
Bifurcation and Chaos
Journal of Difference Equations and Applications
Current Research Projects
See: http://yorke.umd.edu/current-projects.html
Publications
A.
Books:
1984 H. W. Hethcote and J. A. Yorke,
Gonorrhea Transmission Dynamics and Control, Springer-Verlag Lecture Notes in Biomathematics #56, 1984.
1994 E. Ott, T. Sauer and J. A. Yorke,
Coping with Chaos, 1994 John Wiley & Sons, Inc.
1997 K. Alligood, T. Sauer and J. A. Yorke,
Chaos:
An Introduction to Dynamical Systems,
1997 H. E. Nusse and J. A. Yorke,
Dynamics:
Numerical Explorations, Applied Mathematical Sciences 101,
1997
C. Grebogi and. J. A. Yorke, Editors,
The Impact of Chaos on Science and Society,
United Nations University Press, Tokyo (1997). ISBN 92-808-0882-6.
B. Journal Papers
1967
1. A. Strauss and J. A. Yorke, Perturbation theorems for ordinary differential equations, J. Differential Equations 1 (1967), 15-30.
2. J. A. Yorke, Invariance for ordinary differential equations. Math. Systems Theory 1 (1967), 353‑372.
3. A. Strauss and J. A. Yorke, On asymptotically autonomous differential equations. Math. Systems Theory 1 (1967), 175-182.
1968
1. A. Strauss and J. A. Yorke, Perturbing asymptotically stable differential equations, Bull. Amer. Math. Soc. 74 (1968), 992-996. Announcement of #1969-7.
2. J. A. Yorke, Extending Lyapunov's second method to non-Lipschitz Lyapunov functions, Bull. Amer. Math. Soc. 74 (1968), 322-325. Announcement of #1970-3.
1969
1. J. A. Yorke, Permutations and two sequences with the same cluster set, Proc. Amer. Math. Soc. 20 (1969), 606.
2. Elliot Winston and J. A. Yorke, Linear delay differential equations whose solutions become identically zero, Rev. Roumaine Math. Pures Appl. 14 (1969), 885-887.
Abstract: Linear delay differential equations with the property that all solutions become identically zero after a finite period of time are discussed.
3. A. Strauss and J. A. Yorke, Identifying perturbations which preserve asymptotic stability, Proc. Amer. Math. Soc. 22 (1969), 513-518.
4. N. P. Bhatia, G. P. Szego and J. A. Yorke, A Lyapunov characterization of attractors, Boll. Un. Mat. Ital. 4 (1969), 222-228.
Abstract: Necessary and sufficient conditions for a compact set to be respectively a global weak attractor and global attractor for the dynamical system defined by an ordinary differential equation are proved. These conditions are given by means of lower-semicontinuous Liapunov functions.
5. G. S. Jones and J. A. Yorke, The existence and nonexistence of critical points in bounded flows, J. Differential Equations 6 (1969), 238-247.
6. A. Strauss and J. A. Yorke,
On the fundamental theory of differential equations,
7. A. Strauss and J. A. Yorke, Perturbing uniform asymptotically stable non-linear systems, J. Differential Equations 6 (1969), 452-483. Announcement in #1968-1.
8. A. Strauss and J. A. Yorke, Perturbing uniformly stable linear systems with and without attraction, SIAM J. Appl. Math. 17 (1969), 725-739.
9. J. A. Yorke, Non-continuable solutions of differential-delay equations, Proc. Amer. Math. Soc. 21 (1969), 648-652.
Note. This paper discusses differential delay equations x’ = G(xT) with continuous G but with highly non-unique solutions of initial value problems. As a side issue, this paper contains a short proof of the Tietze Extension Theorem on metric spaces. If g is continuous on a closed set S in a metric space X, then define G = g on S and for x not in S,
G(x) = inf for y in S of {g(y) + d(x,y)/d(x,S) – 1}. Then G is continuous on X.
The Tietze extension proof is for functions with a lower bound.
10. J. A. Yorke, Periods of periodic solutions and the Lipschitz constant, Proc. Amer. Math. Soc. 22 (1969), 509-512.
Abstract. Assume dx/dt = F(x) is a differential equation on Rn or on a Hilbert space. Assume F satisfies the Lipshitz condition
|| F(x) – F(y) || ≤ L || x – y || where || . || denotes the Euclidean metric.
Assume p is a periodic orbit with period T. Then T ≥ 2 pi / L.
1970
1. J. A. Yorke, Asymptotic stability for one-dimensional differential delay-equations, J. Differential Equations 7 (1970), 189-202.
2. J. A. Yorke, A continuous differential equation in Hilbert space without existence, Funkcialaj Ekvacioj 13 (1970), 19-21.
3. J. A. Yorke, Differential inequalities and non-Lipschitz scalar functions, Math. Systems Theory 4 (1970), 140-153.
4. Gerald S. Goodman and J. A. Yorke, Misbehavior of solutions of the differential equation dy/dx = f(x,y) + epsilon, when the right side is discontinuous, Mathematica Scandinavica 27 (1970), 72-76.
Abstract: It is well known that by consideration of the corresponding integral equation, most qualitative theorems concerning initial-value problems for the first order ordinary differential equation dy/dx = f (x,y) can be extended to the case where the right side is no longer continuous. In this note, however, we shall show by example that more than one widely used theorem in the continuous case cannot be so extended, at least not in a form that would preserve its most useful feature, as soon as the right side of the equation fails to be jointly continuous at just a single point, even though it remains bounded and continuous there in each variable separately.
5. A. Strauss and J. A. Yorke, Linear perturbations of ordinary differential equations , Proc. Amer. Math. Soc. 26 (1970), 255-260.
Abstract: We present several results dealing with the problem of the preservation of the stability of a system dx/dt=A(t)x that is subject to linear perturbations B(t)x, or to perturbations dominated by linear ones.
6. J. A. Yorke, A theorem on Lyapunov functions using the second derivative of V, Math. Systems Theory 4 (1970), 40-45.
1971
1. A. Lasota and J. A. Yorke, Oscillatory solutions of a second order ordinary differential Equation, Ann. Polon. Math. 25 (1971), 175-178.
2. J. A. Yorke, Another proof of the Lyapunov convexity theorem, SIAM J. Control (1971), 9 351-353.
Abstract: A new proof of the Liapunov convexity theorem is presented.
3. S. Saperstone and J. A. Yorke, Controllability of linear oscillatory systems using positive controls, SIAM J. Control 9 (1971), 253-272.
Abstract: A linear autonomous control process is considered where the null control is an extreme point of the restraint set S. In the even that S=[0,1] (hence, scalar control) necessary and sufficient conditions are given so that the reachable set from the origin (in phase space) contains the origin as an interior point. For vector-valued controls with each component in [0,1], sufficient conditions are given so that the reachable set from the origin of a nonlinear autonomous control process contains the origin as an interior point.
4. A. Lasota and J. A. Yorke, Bounds for periodic solutions of differential equations in Banach spaces, J. Differential Equations 10 (1971), 83-91.
1972
1. A. Lasota and J. A. Yorke, Existence of solutions of two-point boundary value problems for nonlinear systems, J. Differential Equations 11 (1972), 509-518.
2. J. A. Yorke, The maximum principle and controllability of nonlinear equations, SIAM J. Control 10 (1972), 334-338.
Abstract: The main result proved is that a nonlinear control equation is controllable if a related linear equation is controllable. The result allows the set of control values to be discrete and it is not assumed that small values of the control are available. The methods used are closely related to the Pontryagin maximum principle.
3. S. Grossman and J. A. Yorke, Asymptotic behavior and stability criteria for differential delay equations), J. Differential Equations 12 (1972), 236-255.
4. S. Bernfeld and J. A. Yorke, The behavior of oscillatory solutions of x"(t)+p(t)g(x(t))=0, SIAM J. Math. Anal. 3 (1972), 654-667.
Abstract: Various quantitative properties of oscillatory solutions of the scalar second order nonlinear differential equation are obtained under appropriate hypotheses on p and g. In particular, letting {ti, 0 < ti < ti+1, where ti goes to infinity, be the zeroes of any solution x(t), we obtain inequalities that yield asymptotic behavior on x(t). For example, it is shown that the integral of g(x(ti)) exists and is finite: moreover, assuming an added growth condition on g(x)/x, we have then that the integral of x(t) from 0 to infinity exists and is finite.
1973
1. F. W. Wilson, Jr. and J. A. Yorke, Lyapunov functions and isolating blocks, J. Differential Equations 13 (1973), 106-123.
2. K. Cooke and J. A. Yorke, Some equations modelling growth processes and gonorrhea epidemics, Math. Biosci. 16 (1973), 75-101.
Abstract: At the present time VD is a major national problem. Essentially we are confronted with several epidemics. This paper is devoted to a study of processes of this nature. It is hoped that understanding of the mathematical nature of these processes will help in their control.
3,4. W. London, M.D. and J. A. Yorke, Recurrent outbreaks of measles, chicken pox, and mumps, I. Seasonal variation in contact rates, and II. Systematic differences in contact rates and stochastic effects, Amer. J. Epidemiology 98 (1973), 453-468 and 469-482.
5. A. Lasota and J. A. Yorke, The generic property of existence of solutions of differential equations in Banach space, J. Differential Equations 13 (1973), 1-12.
6. A. Lasota and J. A. Yorke, On the existence of invariant measures for piecewise monotonic transformations, Trans. Amer. Math. Soc. 186 (1973), 481-488.
Abstract: A class of piecewise continuous, piecewise C1 transformations on the interval [0,1] is shown to have absolutely continuous invariant measures. This is the first paper to show the existence of invariant measures defined on part of a space by taking Lebesgue measure on the whole space and pushing it forward. This result shows the existence of invariant measures for maps such as the tent map with slope s where 1 < s ≤ 1. Such measures were later called SRB measures when the limit measure is unique. This paper also shows that if the map has slope 1 at one point, there need be no invariant measure.
7. J. A. Yorke and W. N. Anderson, Predator-prey patterns, Proc. Nat. Acad. Sci. 70 (1973), 2069-2071.
Abstract: A graph-theoretic condition is given for the existence of stable solutions to the Volterra-Lotka equations.
1974
1. S. N. Chow and J. A. Yorke, Lyapunov theory and perturbations of stable and asymptotically stable systems, J. Differential Equations 15 (974), 308-321.
2. J. L. Kaplan and J. A. Yorke, Ordinary differential equations which yield periodic solutions of differential delay questions, J. Math. Anal. Appl. 48 (1974), 317-324.
3. J. L. Kaplan, A. Lasota and J. A. Yorke, An application of the Wazewski retract method to boundary value problems, Zeszyty Nauk. Uniw. Jagiellon 356 (1974), 7-14.
1975
1. J. L. Kaplan and J. A. Yorke, On the stability of a periodic solution of a differential equation, SIAM J. Math. Anal. 6 (1975), 268-282.
Abstract: This paper considers the class of scalar, first order, differential delay equations y'(t) = -f(y(t-1)). It is shown that under certain restrictions there exists an annulus A in the (y(t), y(t-1)) - plane whose boundary is a pair of slowly oscillating periodic orbits and A is asymptotically stable. These results are applied to the frequently studied equation dx/dt = -ax(t-1)[1+ x(t)]. The techniques used are related to the Poincare-Bendixson method, used in the (y(t), y(t-1)) - plane.
2. T. Y. Li and J. A. Yorke, Period three implies chaos, Amer. Math. Monthly 82 (1975), 985-992.
1976
1. J. C. Alexander and J. A. Yorke, The implicit function theorem and the global methods of cohomology, J. Functional Anal. 21 (1976), 330-339.
2. A. Lajmanovich Gergely and J. A. Yorke, A deterministic model for gonorrhea in a nonhomogeneous population, Math. Biosci. 28 (1976), 221-236.
Abstract: The spread of gonorrhea in a population is highly nonuniform. The mathematical model discussed takes this into account, splitting the population into n groups. The asymptotic stability properties are studied.
3. R. B. Kellogg, T. Y. Li and J. A. Yorke, A constructive proof of the Brouwer fixed point theorem and computational results, SIAM J. Numer. Anal. 13 (1976), 473-383.
Abstract: A constructive proof of the Brouwer fixed-point theorem is given, which leads to an algorithm for finding the fixed point. Some properties of the algorithm and some numerical results are also presented.
1977
1. J. L. Kaplan and J. A. Yorke, On the nonlinear differential delay equation dx/dt = -f(x(t), x(t-1)), J. Differential Equations 23 (1977), 293-314.
2. J. L. Kaplan and J. A. Yorke, Competitive exclusion and nonequilibrium coexistence, Amer. Naturalist 111 (1977), 1030-1036.
3. A. Lasota and J. A. Yorke, On the existence of invariant measures for transformations with strictly turbulent trajectories, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astro. Phys.225 (1977), 233-238.
Abstract: A sufficient condition is shown for the existence of nontrivial invariant measures in topological spaces. In particular, it is proved that for any continuous transformation on the real line the existence of a periodic point of period three implies the existence of a continuous invariant measure.
4. J. C. Alexander and J. A. Yorke, Parameterized functions, bifurcation, and vector fields on spheres, Prob. of the Asymptotic Theory of Nonlinear Oscillations Order of the Red Banner, Inst. of Mathematics Kiev 1977, 15-17: Anniversary volume in honor of I. Mitropolsky.
1978
1. T. Y. Li and J. A. Yorke, Ergodic transformations from an interval into itself, Trans. Amer. Math. Soc. 235 (1978), 183-192.
Abstract: A class of piecewise continuous, piecewise C1 transformations on the interval J with finitely many discontinuities n are shown to have at most n invariant measures
2. J. C. Alexander and J. A. Yorke, Global bifurcation of periodic orbits, Amer. J. Math. 100 (1978), 263-292.
3. S. N. Chow, J. Mallet-Paret and J. A. Yorke, Finding zeroes of maps: Homotopy methods that are constructive with probability one, Math. of Comp. 32 (1978), 887-899.
Abstract: We illustrate that most existence theorems using degree theory are in principle relatively constructive. The first one presented here is the Brouwer Fixed Point Theorem. Our method is constructive with probability one and can be implemented by computer. Other existence theorems are also proved by the same method. The approach is based on a transversality theorem.
4. J. A. Yorke, H. W. Hethcote and A. Nold Dynamics and control of the transmission of gonorrhea, Sexually Transmitted Diseases 5 (1978), 51-56.
5. T. Y. Li and J. A. Yorke, Ergodic maps on [0,1] and nonlinear pseudo-random number generators, Nonlinear Anal. 2 (1978), 473-481.
6. S. N. Chow, J. Mallet-Paret and J. A. Yorke, Global Hopf bifurcation from a multiple eigenvalue, Nonlinear Anal. 2 (1978), 753-763.
7. J. C. Alexander and J. A. Yorke, Calculating bifurcation invariants as elements in the homotopy of the general linear group, J. Pure Appl. Algebra 13 (1978), 1-8.
8. J. C. Alexander and J. A. Yorke, The homotopy continuation method: Numerically implementable topological procedures, Trans. Amer. Math. Soc. 242 (1978), 271-284.
Abstract: The homotopy continuation method involves numerically finding the solution of a problem by starting from the solution of a known problem and continuing the solution as the known problem is homotoped to the given problem. The process is axiomatized and an algebraic topological condition is given that guarantees the method will work. A number of examples are presented that involve fixed points, zeroes of maps, singularities of vector fields, and bifurcation. As an adjunct, proofs using differential rather than algebraic techniques are given for the Borsuk-Ulam Theorem and the Rabinowitz Bifurcation Theorem.
9. T. D. Reynolds, W. P. London and J. A. Yorke, Behavioral rhythms in schizophrenia, J. Nervous and Mental Disease 166 (1978), 489-499.
Abstract: Daily behavioral observations were made for several years on 10 male schizophrenic patients and on three male patients with organic brain disorders. Analysis of these data showed strong cyclic components in the five schizophrenic patients with predominantly hebephrenic symptomatology. Period lengths noted were about 2 days, 5 to 6 day, 30 days, and a longer cycle of 40 to 100 days duration. Antipsychotic medications appear to have a suppressant effect, but tricyclic antidepressants may enhance pre-existing rhythms.
1979
1. J. L. Kaplan, M. Sorg and J. A. Yorke, Solutions of dx/dt = f(x(t), x(t-1)) have limits when f is an order relation, Nonlinear Anal. 3 (1979), 53-58.
2. J. L. Kaplan and J. A. Yorke, Nonassociative real algebras and quadratic differential equations, Nonlinear Anal. 3 (1979), 49-51.
3. J. A. Yorke, N. Nathanson, G. Pianigiani and J. Martin, Seasonality and the requirements for perpetuation and eradication of viruses in populations, Amer. J. Epidemiology 109 (1979), 103-123.
4. G. Pianigiani and J. A. Yorke, Expanding maps on sets which are almost invariant: Decay and chaos, Trans. Amer. Math. Soc. 252 (1979), 351-366.
Abstract: Let A be a subset of Rn be a bounded open set with finitely many connected components Aj and let T be a smooth map on Rn with A a subset of T(A). Assume that for each Aj, A is a subset of Tk(Aj) for all k sufficiently large. We assume that T is expansive, but we do not assume that T(A) = A. Hence for x in A, Ti(x) may escape A as i increases. Let m be a smooth measure on A (with inf density > 0) and let x in A be chosen at random (using m). Since T is expansive we may expect Ti(x) to oscillate chaotically on A for a certain time and eventually escape A. For each measurable set E in A define mk(A) to be the conditional probability that Tk(x) is in E given that x, T1(x), ...,Tk (x) are in A. We show that mk converges to a smooth measure m0 that is independent of the choice of m which we call a “conditionally invariant measure”. One-dimensional examples are stressed.
5. J. L. Kaplan and J. A. Yorke, Preturbulence: A regime observed in a fluid flow model of Lorenz, Comm. Math. Phys. 67 (1979), 93-108. This paper is reprinted in Russian in a book edited by Sinai and Kolmogorov on strange attractors.
Abstract: This paper studies a forced, dissipative system of three ordinary differential equations. The behavior of this system, first studied by Lorenz, has been interpreted as providing a mathematical mechanism for understanding turbulence. It is demonstrated that prior to the onset of chaotic behavior there exists a preturbulent state where turbulent orbits exist but represent a set of measure zero