2012/11/20 by Temple He, Salman Habib
Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Control theory (sociology) #Degrees of freedom (physics and chemistry) #Dynamical system (definition) #Dynamical systems theory #Hamiltonian system #Limiting #Lyapunov exponent #Lyapunov function #Noise (video) #Stochastic processes and financial applications #nlin.CD #stochastic dynamics and bifurcation
paper · pdf · doi:10.1063/1.4813864
published as Chaos 23, 033123 (2013) · 11 pages, no figures
arxiv created 2012/11/20 · openalex publication_date 2013/08/15 · arxiv updated 2015/04/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Simple dynamical systems--with a small number of degrees of freedom--can behave in a complex manner due to the presence of chaos. Such systems are most often (idealized) limiting cases of more realistic situations. Isolating a small number of dynamical degrees of freedom in a realistically coupled system generically yields reduced equations with terms that can have a stochastic interpretation. In situations where both noise and chaos can potentially exist, it is not immediately obvious how Lyapunov exponents, key to characterizing chaos, should be properly defined. In this paper, we show how to do this in a class of well-defined noise-driven dynamical systems, derived from an underlying Hamiltonian model.