Abstract
Khasminskii's projection on circles, spheres or hyperspheres leads to the top Lyapunov exponents of dynamic systems. Provided there exists an invariant measure, the multiplicative ergodic theorem of Oseledec can be reduced to a finite integral on the projection angles. This technique is demonstrated by nonlinear deterministic systems with self-exciting terms and by linear systems with parametric excitations by white noise. The paper emphasizes different numerical methods to solve Liouville or Fokker-Planck equations and to determine the invariant measures of dynamic systems.
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© 1991 Springer-Verlag
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Wedig, W. (1991). Lyapunov exponents and invariant measures of equilibria and limit cycles. In: Arnold, L., Crauel, H., Eckmann, JP. (eds) Lyapunov Exponents. Lecture Notes in Mathematics, vol 1486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086678
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DOI: https://doi.org/10.1007/BFb0086678
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