Article Contents

2014, Volume 19, Issue 2: 523-541. Doi: 10.3934/dcdsb.2014.19.523

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Expanding Baker Maps as models for the dynamics emerging from 3D-homoclinic bifurcations

1.
Departamento de Matemáticas, Universidad de Oviedo, Calvo Sotelo s/n, 33007 Oviedo
2.
Dep. de Matemáticas, Universidad de Oviedo, Calvo Sotelo s/n, 33007, Oviedo
3.
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via, 585, 08080 Barcelona

Received: March 2013

Revised: December 2013

Published: March 2014

Abstract / Introduction Related Papers Cited by

Abstract

For certain 3D-homoclinic tangencies where the unstable manifold of the saddle point involved in the homoclinic tangency has dimension two, many different strange attractors have been numerically observed for the corresponding family of limit return maps. Moreover, for some special value of the parameter, the respective limit return map is conjugate to what was called bidimensional tent map. This piecewise affine map is an example of what we call now Expanding Baker Map, and the main objective of this paper is to show how many of the different attractors exhibited for the limit return maps resemble the ones observed for Expanding Baker Maps.

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Mathematics Subject Classification: Primary: 37C70, 37D45; Secondary: 37G35.

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