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Regular and Chaotic Dynamics, 2010, Volume 15, Issue 2-3, Pages 237–245
DOI: https://doi.org/10.1134/S1560354710020115
(Mi rcd491)
 

This article is cited in 6 scientific papers (total in 6 papers)

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

Snap-back repellers in non-smooth functions

L. Gardinia, F. Tramontanab

a University of Urbino, 61029 Urbino, Italy
b Marche Polytechnic University, Piazzale Martelli, 60121 Ancona, Italy
Citations (6)
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.
Received: 15.11.2009
Accepted: 23.12.2009
Bibliographic databases:
Document Type: Personalia
MSC: 37E05, 37G10, 37G15
Language: English
Citation: L. Gardini, F. Tramontana, “Snap-back repellers in non-smooth functions”, Regul. Chaotic Dyn., 15:2-3 (2010), 237–245
Citation in format AMSBIB
\Bibitem{GarTra10}
\by L. Gardini, F. Tramontana
\paper Snap-back repellers in non-smooth functions
\jour Regul. Chaotic Dyn.
\yr 2010
\vol 15
\issue 2-3
\pages 237--245
\mathnet{http://mi.mathnet.ru/rcd491}
\crossref{https://doi.org/10.1134/S1560354710020115}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2644333}
\zmath{https://zbmath.org/?q=an:1203.37069}
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  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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