Chaotic and nonchaotic mushrooms

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January & February 2008, 22(1&2): 63-74. doi: 10.3934/dcds.2008.22.63

Chaotic and nonchaotic mushrooms

1.	ABC Math Program and School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, United States

Received March 2007 Revised May 2008 Published June 2008

Abstract
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In the paper [4] were introduced visual and simple classes of dynamical systems with divided phase space, i.e., with the coexistence of chaotic components of positive measure and islands of regular dynamics. These classes consist of mushroom billiards and their modifications. Here we generalize the construction of mushroom billiards and besides present another class of simple and visual billiards with divided phase space.

Keywords: divided phase space, Hamiltonian systems, hyperbolicity, mushroom billiards..

Mathematics Subject Classification: Primary: 37D50; Secondary: 34D0.

Citation: Leonid A. Bunimovich. Chaotic and nonchaotic mushrooms. Discrete & Continuous Dynamical Systems - A, 2008, 22 (1&2) : 63-74. doi: 10.3934/dcds.2008.22.63

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