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arXiv · 1609.07539

On the Almost Everywhere Stability of Discrete-Time Dynamical Systems

Ozkan Karabacak·Rafael Wisniewski·John-Josef Leth
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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.

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Ozkan Karabacak, Rafael Wisniewski, John-Josef Leth. 2016-09-24. On the Almost Everywhere Stability of Discrete-Time Dynamical Systems. https://arxiv.org/abs/1609.07539

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