Lyapunov exponents for small random perturbations of Hamiltonian systems

Annals of Probability

Volumn 30, Issue 1, 2002, Pages 101-134

  Baxendale, Peter H ^a   Goukasian, Levon ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

Hamiltonian; Lyapunov exponent; Nilpotent stochastic differential equation; Stochastic averaging; Stochastic oscillator

Indexed keywords

EID: 0035993030     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1020107762     Document Type: Article

References (25)

1. Lyapunov exponent and rotation number of a two-dimensional nilpotent stochastic system
2. Asymptotic analysis of the Lyapunov exponent and rotation number of the random oscillator and applications
3. Toward an understanding of the stochastic Hopf bifurcation: A case study
4. Asymptotic expansions of the Liapunov index for linear stochastic systems with small noise
5. Statistical equilibrium and two-point motion for a stochastic flow of diffeomorphisms
6. A stochastic Hopf bifurcation
7. Stability along trajectories at a stochastic bifurcation point
8. Lyapunov exponents of nilpotent Itô systems with random coefficients
9. Large deviations and stochastic flows of diffeomorphisms
10. Random perturbations of nonlinear oscillators
11. A remark on random perturbations of the nonlinear pendulum
12. Random perturbations of Hamiltonian systems
13. An explicit description of the Lyapunov exponents of the noisy damped harmonic oscillator
14. Numerical approximation of random attractors
15. The behavior of a conservative system under the action of slight friction and slight random noise
16. P-bifurcations in the noisy Duffing-van der Poi equation
17. Stability of Markovian processes III: Foster-Lyapunov criteria for continuous time processes
18. Lyapunov exponents of nilpotent Itô systems
19. A control problem related to the Lyapunov spectrum of stochastic flows
20. Bifurcation scenarios of the noisy Duffing-van der Pol oscillator
21. On the tangent flow of a stochastic differential equation with fast drift
22. Lyapunov exponents and invariant measures of equilibria and limit cycles