Showing papers by "Lai Sang Young published in 2003"

Entropy in dynamical systems

Abstract: In this article, the word entropy is used exclusively to refer to the entropy of a dynamical system, ie a map or a flow It measures the rate of increase in dynamical complexity as the system evolves with time This is not to be confused with other notions of entropy connected with spatial complexity I will attempt to give a brief survey of the role of entropy in dynamical systems and especially in smooth ergodic theory The topics are chosen to give a flavor of this invariant; they are also somewhat biased toward my own interests This article is aimed at nonexperts After a review of some basic definitions and ideas, I will focus on one main topic, namely the relation of entropy to Lyapunov exponents and dimension, which I will discuss in some depth Several other interpretations of entropy, including its relations to volume growth, periodic orbits and horseshoes, large deviations and rates of escape are treated briefly

Strange Attractors in Periodically-Kicked Limit Cycles and Hopf Bifurcations

Abstract: We prove the emergence of chaotic behavior in the form of horseshoes and strange attractors with SRB measures when certain simple dynamical systems are kicked at periodic time intervals. The settings considered include limit cycles and stationary points undergoing Hopf bifurcations.