Hyperbolic invariant sets of the real generalized Hénon maps

Xu Zhang

Chaos, Solitons & Fractals, 2010, vol. 43, issue 1, 31-41

Abstract: In this paper, the conditions under which there exists a uniformly hyperbolic invariant set for the generalized Hénon map F(x,y)= (y,ag(y)−δx) are investigated, where g(y) is a monic real-coefficient polynomial of degree d⩾2, a and δ are non-zero parameters. It is proved that for certain parameter regions the map has a Smale horseshoe and a uniformly hyperbolic invariant set on which it is topologically conjugate to the two-sided fullshift on two symbols, where g(y) has at least two different non-negative or non-positive real zeros, and ∣a∣ is sufficiently large. Moreover, it is shown that if g(y) has only simple real zeros, then for sufficiently large ∣a∣, there exists a uniformly hyperbolic invariant set on which F is topologically conjugate to the two-sided fullshift on d symbols.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:43:y:2010:i:1:p:31-41

DOI: 10.1016/j.chaos.2010.07.003

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