Conservative Homoclinic Bifurcations and Some Applications

A. Gorodetski ; V. Kaloshin

Informatics and Automation, Singularities and applications, Tome 267 (2009), pp. 82-96.

Résumé

We study generic unfoldings of homoclinic tangencies of two-dimensional area-preserving diffeomorphisms (conservative Newhouse phenomena) and show that they give rise to invariant hyperbolic sets of arbitrarily large Hausdorff dimension. As applications, we discuss the size of the stochastic layer of a standard map and the Hausdorff dimension of invariant hyperbolic sets for certain restricted three-body problems. We avoid involved technical details and only concentrate on the ideas of the proof of the presented results.

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