Shilnikov-type dynamics in three-dimensional piecewise smooth maps. (English) Zbl 1483.37060
Summary: 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 eigenmanifolds 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.
MSC:
| 37G20 | Hyperbolic singular points with homoclinic trajectories in dynamical systems |
| 37G35 | Dynamical aspects of attractors and their bifurcations |
Keywords:
three dimensional piecewise smooth map; Shilnikov chaos; stable manifold and unstable manifoldReferences:
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