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Valentín Mendoza

Universidade Federal de Itajubá


Mendoza V.
The Dynamical Core of a Homoclinic Orbit
2022, vol. 27, no. 4, pp.  477-491
The complexity of a dynamical system exhibiting a homoclinic orbit is given by its dynamical core which, due to Cantwell, Conlon and Fenley, is a set uniquely determined in the isotopy class, up to a topological conjugacy, of the end-periodic map relative to that orbit. In this work we prove that a sufficient condition to determine the dynamical core of a homoclinic orbit of a Smale diffeomorphism on the 2-disk is the non-existence of bigons relative to this orbit. Moreover, we propose a pruning method for eliminating bigons that can be used to find a Smale map without bigons and hence for finding the dynamical core.
Keywords: Homoclinic orbits, dynamical core, Smale horseshoe, pruning theory
Citation: Mendoza V.,  The Dynamical Core of a Homoclinic Orbit, Regular and Chaotic Dynamics, 2022, vol. 27, no. 4, pp. 477-491

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