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On Lyapunov Exponents and Rotation Number of Random Linear Hamiltonian Systems
Author(s) -
Teichert Heidrun
Publication year - 1993
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19931640106
Subject(s) - lyapunov exponent , mathematics , ergodic theory , rotation number , hamiltonian (control theory) , hamiltonian system , markov chain , lagrangian , exponent , mathematical analysis , pure mathematics , mathematical physics , nonlinear system , quantum mechanics , physics , invariant (physics) , statistics , mathematical optimization , linguistics , philosophy
We consider linear Hamiltonian differential systems in R 2 n depending on a stationary ergodic Markov process. The induced processes on the Lagrangian manifolds L p and L p −1, p (1 ≦ p ≦ n ) are studied. From this we derive representations for the Lyapunov exponents, especially the lowest non‐negative exponent, and a (suitably defined) rotation number of the system.