Abstract
We discuss a geometric configuration for a class of homeomorphisms in \({\mathbb{R}^3}\) producing the existence of infinitely many periodic points as well a complex dynamics due to the presence of a topological horseshoe. We also show that such a class of homeomorphisms appears in the classical Lotka–Volterra system.
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ERC Starting Investigator Grant No. 259559, EPIDELAY. The research of A. R.-H. was performed in the framework of the TÁMOP 4.2.4.A/2-11-1-2012-0001 “National Excellence Programme Elaborating and operating an inland student and researcher personal support system convergence programme” Control tools in biology, which is subsidized by the European Union and Hungary and co-financed by the European Social Fund. The research of F. Z. was performed under the auspices of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).
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Ruiz-Herrera, A., Zanolin, F. Horseshoes in 3D equations with applications to Lotka–Volterra systems. Nonlinear Differ. Equ. Appl. 22, 877–897 (2015). https://doi.org/10.1007/s00030-014-0307-9
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DOI: https://doi.org/10.1007/s00030-014-0307-9