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• W2956098402 abstract "Chaotic attractors in the two-dimensional border-collision normal form (a piecewise-linear map) can persist throughout open regions of parameter space. Such robust chaos has been established rigorously in some parameter regimes. Here we provide formal results for robust chaos in the original parameter regime of [S. Banerjee, J.A. Yorke, C. Grebogi, Robust Chaos, Phys. Rev. Lett. 80(14):3049--3052, 1998]. We first construct a trapping region in phase space to prove the existence of a topological attractor. We then construct an invariant expanding cone in tangent space to prove that tangent vectors expand and so no invariant set can have only negative Lyapunov exponents. Under additional assumptions we also characterise an attractor as the closure of the unstable manifold of a fixed point." @default.
• W2956098402 created "2019-07-12" @default.
• W2956098402 creator A5067953112 @default.
• W2956098402 creator A5084524431 @default.
• W2956098402 date "2019-06-27" @default.
• W2956098402 modified "2023-10-01" @default.
• W2956098402 title "Constructing robust chaos: invariant manifolds and expanding cones" @default.
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