The "0 to ∞-homoclinic bifurcation" of a class of discrete two-dimensional maps

Flaviano Battelli; Claudio Lazzari

Published: 1999-09-30

Vol. 13 (1999)

The "0 to ∞-homoclinic bifurcation" of a class of discrete two-dimensional maps

Flaviano Battelli , Claudio Lazzari

Abstract

Based on a previous theoretical result of the same authors the presen paper deals with discrete perturbed two-dimensional maps having a semi-hyperbolic fixed point. We give applicable sufficient conditions assuring a particular kind of bifurcation of homoclinic orbits when the perturbative parameter μ varies in a small neighborhood of zero: no homoclinic orbits when μ is on one side of zero, one homoclinic orbit when μ = 0, and infinite homoclinics when μ is on the other side of zero.

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Battelli, F., & Lazzari, C. (1999). The "0 to ∞-homoclinic bifurcation" of a class of discrete two-dimensional maps. Annales Mathematicae Silesianae, 13, 73–80. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14138

Flaviano Battelli

Affiliation:

Dipartimento di Matematica " V. Volterra", Facoltá di Ingegneria, Universitá di Ancona, Italy Italy

Claudio Lazzari

c.lazzari@mat.uniurb.it

Affiliation:

Facoltá di Scienze MM.FF.NN., Universitá di Urbino, Italy Italy

Vol. 13 (1999)
Published: 1999-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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