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The Kullback-Liebler Divergence as a Lyapunov Function for Incentive Based Game Dynamics
The Kullback-Liebler Divergence Lyapunov Function Incentive Game Dynamics Dynamical Systems
2012/7/9
It has been shown that the Kullback-Leibler divergence is a Lyapunov function for the replicator equations at evolutionary stable states, or ESS. In this paper we extend the result to a more general c...
Multifractal analysis of some multiple ergodic averages for the systems with non-constant Lyapunov exponents
Multifractal analysis of some multiple ergodic averages non-constant Lyapunov exponents Dynamical Systems
2012/6/27
We study certain multiple ergodic averages of an iterated functions system generated by two contractions on the unit interval. By using the dynamical coding ${0,1}^{\mathbb{N}}$ of the attractor, we c...
Entropy, Lyapunov exponents and the volume growth of boundary distortion under the action of dynamical systems
Lyapunov exponents the volume growth of boundary distortion the action of dynamical systems
2012/4/17
We study the connection between the Lyapunov exponents and the volume growth of boundary distortion of regions in the phase space of the dynamical system.
Morse decomposition and Lyapunov functions for dynamical systems
Differential equation and dynamical system Morse decomposition Lyapunov function
2011/10/18
In this paper, we review Morse decomposition and Lyapunov functions. Most of the results are due to Conley and are known. Attractor-repeller pairs and Morse decompositions are very useful to study the...
Existence of complete Lyapunov functions for semiflows on separable metric spaces
Lyapunov functions Semiflows Separable metric space
2011/9/23
Abstract: The aim of this short note is to show how to construct a complete Lyapunov function of a semiflow by using a complete Lyapunov function of its time-one map. As a byproduct we assure the exis...
Entropy, Lyapunov Exponents and Escape Rates in Open Systems
Lyapunov Exponents Escape Rates Open Systems Dynamical Systems
2011/9/5
Abstract: We study the relation between escape rates and pressure in general dynamical systems with holes, where pressure is defined to be the difference between entropy and the sum of positive Lyapun...