On the Almost Everywhere Stability of Discrete-Time Dynamical Systems
Adaptation and Self-Organizing Systems
2018-03-12 v3 Dynamical Systems
Abstract
For a dynamical system, it is known that the existence of a Lyapunov-type density function, called Lyapunov density or Rantzer's density function, implies convergence of Lebesgue almost all solutions to an equilibrium. Using the duality between Frobenius-Perron and Koopmann operators, we generalize this result from equilibrium to invariant sets, both for continuous- and discrete-time. Furthermore, some redundant assumptions that exist in the literature of almost everywhere stability for discrete-time, such as the local stability of the attractor and the compactness of the state space, has been removed.
Keywords
Cite
@article{arxiv.1609.07539,
title = {On the Almost Everywhere Stability of Discrete-Time Dynamical Systems},
author = {Ozkan Karabacak and Rafael Wisniewski and John-Josef Leth},
journal= {arXiv preprint arXiv:1609.07539},
year = {2018}
}