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• W2063388951 abstract "By a classical theorem transversal homoclinic points of maps leadto shift dynamics on a maximal invariant set, also referred to asa homoclinic tangle. In this paper we study the fate ofhomoclinic tangles in parameterized systems from the viewpoint ofnumerical continuation and bifurcation theory. The newbifurcation result shows that the maximal invariant set near ahomoclinic tangency, wheretwo homoclinic tangles collide, can be characterized by a systemof bifurcation equations that is indexed by a symbolic sequence.These bifurcation equations consist of a finite or infinite set ofhilltop normal forms known from singularity theory.For the Henon family we determine numerically the connected componentsof branches with multi-humped homoclinic orbits that pass through several tangencies.The homoclinic network found by numerical continuation is explainedby combining our bifurcation result with graph-theoretical arguments." @default.
• W2063388951 created "2016-06-24" @default.
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• W2063388951 date "2014-01-01" @default.
• W2063388951 modified "2023-10-18" @default.
• W2063388951 title "Continuation and collapse of homoclinic tangles" @default.
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• W2063388951 doi "https://doi.org/10.3934/jcd.2014.1.71" @default.
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