Frontiers of Mathematics in China >
Rapid fluctuation for topological dynamical systems
Received date: 26 Aug 2008
Accepted date: 20 Oct 2008
Published date: 05 Sep 2009
Copyright
In this paper, we introduce a new notion called rapid fluctuation to characterize the complexity of a general topological dynamical system. As a continuation of the former work [Huang, Chen, Ma, J. Math. Anal. Appl., 2006, 323: 228-252], here we prove that a Lipschitz dynamical system defined on a compact metric space has a rapid fluctuation if it has either a quasi shift invariant set or a topological horseshoe. As an application, the rapid fluctuation of a discrete predator-prey model is considered.
Yu HUANG , Yi ZHOU . Rapid fluctuation for topological dynamical systems[J]. Frontiers of Mathematics in China, 2009 , 4(3) : 483 -494 . DOI: 10.1007/s11464-009-0030-8
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