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On the dynamics of non-autonomous systems in a neighborhood of a homoclinic trajectory
Calamai, Alessandro
Franca, Matteo
Pospíšil, Michal
2024
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e-ISSN
2464-8728
Abstract
This article is devoted to the study of a 2-dimensional piecewise smooth (but possibly) discontinuous dynamical system, subject to a non-autonomous perturbation; we assume that the unperturbed system admits a homoclinic trajectory ⃗γ(t). Our aim is to analyze the dynamics in a neighborhood of ⃗γ(t) as the perturbation is turned on, by defining a Poincar´e map and evaluating fly time and space displacement of trajectories performing a loop close to ⃗γ(t). Besides their intrinsic mathematical interest, these results can be thought of as a first step in the analysis of several interesting problems, such as the stability of a homoclinic trajectory of a non-autonomous ODE and a possible extension of Melnikov chaos to a discontinuous setting.
Source
Alessandro Calamai, Matteo Franca and Michal Pospíšil, "On the dynamics of non-autonomous systems in a neighborhood of a homoclinic trajectory" in: "Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.56 (2024)", EUT Edizioni Università di Trieste, Trieste, 2024, pp. 143-209
Languages
en
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
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