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Snap-back repellers in non-smooth functions

  • L.P. Shilnikov-75
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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.

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Authors and Affiliations

  1. University of Urbino, 61029, Urbino, Italy

    L. Gardini

  2. Marche Polytechnic University, Piazzale Martelli, 60121, Ancona, Italy

    F. Tramontana

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  1. L. Gardini
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  2. F. Tramontana
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Correspondence to L. Gardini.

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Gardini, L., Tramontana, F. Snap-back repellers in non-smooth functions. Regul. Chaot. Dyn. 15, 237–245 (2010). https://doi.org/10.1134/S1560354710020115

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