The asymptotic stability of weakly perturbed two dimensional hamiltonian systems

Ludwig Arnold, Peter Imkeller, N. Sri Namachchivaya

Research output: Contribution to conferencePaperpeer-review

Abstract

The purpose of this work is to obtain an approximation for the top Lyapunov exponent, the exponential growth rate, of the response of a single-well Kramers Oscillator driven by either a multiplicative or an additive white noise process. To this end, we consider the equations of motion as dissipative and noisy perturbations of a two-dimensional Hamiltonian system. A perturbation approach is used to obtain explicit expressions for the exponent in the presence of small intensity noise and small dissipation. We show analytically that the top Lyapunov exponent is positive, and for small values of noise intensity √ε and dissipation ε the exponent grows proportional to ε1/3.

Original languageEnglish (US)
Pages2477-2486
Number of pages10
StatePublished - 2001
Event18th Biennial Conference on Mechanical Vibration and Noise - Pittsburgh, PA, United States
Duration: Sep 9 2001Sep 12 2001

Other

Other18th Biennial Conference on Mechanical Vibration and Noise
Country/TerritoryUnited States
CityPittsburgh, PA
Period9/9/019/12/01

ASJC Scopus subject areas

  • Modeling and Simulation
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design

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