On Topological and Hyperbolic Properties of Systems with Homoclinic Tangencies
We study dynamical properties of a set Λ of trajectories from a small neighbourhood of a non-transversal Poincaré homoclinic orbit. We show that this problem has no univalent solution, as it takes place in the case of a transversal homoclinic orbit. Here different situations are possible, depending on the character of the homoclinic tangency, when Λ is trivial or contains topological (hyperbolic) horseshoes. In this chapter we find certain conditions for existence of both types of dynamics and give a description (in term of the symbolic dynamics) of the corresponding non-trivial hyperbolic subsets from Λ.
KeywordsInvariant Manifold Homoclinic Orbit Finite Order Symbolic Dynamic Homoclinic Point
The authors thank M. Malkin and D. Turaev for very fruitful discussions. AG and SG have been partially supported by the Russian Scientific Foundation Grant 14-41-00044 and the grants of RFBR No.13-01-00589, 13-01-97028-povolzhye and 14-01-00344. ML was partially supported by a NSC research grant.
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