Lyapunov exponents for discontinuous differential equations
Authors:
B. S. Berger and M. Rokni
Journal:
Quart. Appl. Math. 48 (1990), 549-553
MSC:
Primary 34D08
DOI:
https://doi.org/10.1090/qam/1074970
MathSciNet review:
MR1074970
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Abstract: The vector field associated with a dynamical system is assumed to be piecewise continuously differentiable. The gradient of the vector field, entering into integral expressions for the Lyapunov exponents, may therefore contain derivatives of step functions. Results from the theory of distributions are used in the integrals’ evaluation.
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J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, 1983
Y. Z. Tsypkin, Relay Control Systems, Cambridge University Press, 1984
A. A. Andronov, E. A. Vitt, and S. E. Khaiken, Theory of Oscillators, Pergammon Press, 1966
G. Benettin, L. Galagani, A. Giorgilli, and J. Strelcyn, Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems: method for computing all of them, Meccanica 15, 9–20 (1980)
J. Shimada and T. Nagashima, A numerical approach to the ergodic problem of dissipative dynamical systems, Prog. in Theoretical Physics (6) 61, 1605–1616 (1979)
B. S. Berger and M. Rokni, Lyapunov exponents and continuum kinematics, Int. J. Engrg. Sci. 25, 1079–1084 (1987)
A. C. Eringen, Continuum Physics, vol. II, Academic Press, 1975
A. H. Zemanian, Distribution Theory and Transform Analysis, McGraw-Hill, 1965
D. H. Griffel, Applied Functional Analysis, Ellis Horwood Limited, 1981
M. Rokni and B. S. Berger, Lyapunov exponents and subspace evolution, Quart. Appl. Math. (4) 45, 789–793 (1987)
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© Copyright 1990
American Mathematical Society
