The Homoclinic Tangle and Smale’s Horseshoe Map
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منابع مشابه
On the Dynamics of Certain Homoclinic Tangles
In this paper we study homoclinic tangles formed by transversal intersections of the stable and the unstable manifold of a non-resonant, dissipative homoclinic saddle point in periodically perturbed second order equations. We prove that the dynamics of these homoclinic tangles are that of infinitely wrapped horseshoe maps (See Section 1A). Using μ as a parameter representing the magnitude of th...
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Global results are proved about the way in which Boyland’s forcing partial order organizes a set of braid types: those of periodic orbits of Smale’s horseshoe map for which the associated train track is a star. This is a special case of a conjecture introduced in [dCHb], which claims that forcing organizes all horseshoe braid types into linearly ordered families which are, in turn, parameterize...
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◦ Geodesic flows on compact manifolds with negative sectional curvature. Later, we relax uniform hyperbolicity to an asymptotic one, called non-uniform hyperbolicity. Two examples of such systems are: ◦ Slow down of fA : T → T, see [9]. ◦ Geodesic flows on surfaces with nonpositive curvature. Introductory example: Smale’s horseshoe [21]. Let g : K → K be Smale’s horseshoe map, and σ : Σ→ Σ the ...
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An important problem in the dynamics of surface homeomorphisms is determining the forcing relation between orbits. The forcing relation between periodic orbits can be computed using existing algorithms. Here we consider forcing relations between homoclinic orbits. We outline a general procedure for computing the forcing relation, and apply this to compute the equivalence and forcing relations f...
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تاریخ انتشار 2011