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arXiv · 1903.10781

Shilnikov-type Dynamics in Three-Dimensional Piecewise Smooth Maps

Indrava Roy·Mahashweta Patra·Soumitro Banerjee
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Abstract

We show the existence of Shilnikov-type dynamics and bifurcation behaviour in general discrete three-dimensional piecewise smooth maps and give analytical results for the occurence of such dynamical behaviour. Our main example in fact shows a `two-sided' Shilnikov dynamics, i.e. simultaneous looping and homoclinic intersection of the one-dimensional eigenmanfolds of fixed points on both sides of the border. We also present two complementary methods to analyse the return time of an orbit to the border: one based on recursion and another based on complex interpolation.

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Indrava Roy, Mahashweta Patra, Soumitro Banerjee. 2019-03-26. Shilnikov-type Dynamics in Three-Dimensional Piecewise Smooth Maps. https://doi.org/10.1016/j.chaos.2020.109655

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