Displaying similar documents to “Heterodimensional cycles, partial hyperbolicity and limit dynamics”

Non-uniformly hyperbolic horseshoes arising from bifurcations of Poincaré heteroclinic cycles

Jacob Palis, Jean-Christophe Yoccoz (2009)

Publications Mathématiques de l'IHÉS

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In the present paper, we advance considerably the current knowledge on the topic of bifurcations of heteroclinic cycles for smooth, meaning C ∞, parametrized families {g t ∣t∈ℝ} of surface diffeomorphisms. We assume that a quadratic tangency q is formed at t=0 between the stable and unstable lines of two periodic points, not belonging to the same orbit, of a (uniformly hyperbolic) horseshoe K (see an example at the Introduction) and that such lines cross each other with positive relative...

C¹-maps having hyperbolic periodic points

N. Aoki, Kazumine Moriyasu, N. Sumi (2001)

Fundamenta Mathematicae

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We show that the C¹-interior of the set of maps satisfying the following conditions: (i) periodic points are hyperbolic, (ii) singular points belonging to the nonwandering set are sinks, coincides with the set of Axiom A maps having the no cycle property.

Partial hyperbolicity and homoclinic tangencies

Sylvain Crovisier, Martin Sambarino, Dawei Yang (2015)

Journal of the European Mathematical Society

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We show that any diffeomorphism of a compact manifold can be C 1 approximated by diffeomorphisms exhibiting a homoclinic tangency or by diffeomorphisms having a partial hyperbolic structure.

The explosion of singular cycles

Rodrigo Bamon, Rafael Labarca, Ricardo Mañé, Maria-José Pacífico (1993)

Publications Mathématiques de l'IHÉS

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Simple examples of one-parameter planar bifurcations.

Armengol Gasull, Rafel Prohens (2000)

Extracta Mathematicae

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In this paper we give simple and low degree examples of one-parameter polynomial families of planar differential equations which present generic, codimension one, isolated, compact bifurcations. In contrast with some examples which appear in the usual text books each bifurcation occurs when the bifurcation parameter is zero. We study the total number of limit cycles that the examples present and we also make their phase portraits on the Poincaré sphere.