This article is cited in 8 papers

On the 75th birthday of Professor L.P. Shilnikov

Snap-back repellers in non-smooth functions

L. Gardini^a, F. Tramontana<sup>b

a</sup> University of Urbino, 61029 Urbino, Italy
^b Marche Polytechnic University, Piazzale Martelli, 60121 Ancona, Italy

Abstract: In this work we consider the homoclinic bifurcations of expanding periodic points. After Marotto, when homoclinic orbits to expanding periodic points exist, the points are called snap-back-repellers. Several proofs of the existence of chaotic sets associated with such homoclinic orbits have been given in the last three decades. Here we propose a more general formulation of Marotto’s theorem, relaxing the assumption of smoothness, considering a generic piecewise smooth function, continuous or discontinuous. An example with a two-dimensional smooth map is given and one with a two-dimensional piecewise linear discontinuous map.

Keywords: snap back repellers, homoclinic orbits in noninvertible maps, orbits homoclinic to expanding points.

MSC: 37E05, 37G10, 37G15

Received: 15.11.2009
Accepted: 23.12.2009

Language: English

DOI: 10.1134/S1560354710020115

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