A computer-assisted proof of the existence of Smale horseshoe for the folded-towel map
نویسندگان
چکیده
The paper contains a rigorous proof of existence symbolic dynamics chaos in the generalized H\'enon map's 4th iterate $H^4$, which was conjectured \textit{A 3D Smale Horseshoe Hyperchaotic Discrete-Time System} Li and Yang, 2007. We prove also uniform hyperbolicity invariant set with dynamics. proofs are computer-assisted use C++ library \textit{CAPD} for interval arithmetic, differentiation integration.
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15 صفحه اولForcing Relations for Homoclinic Orbits of the Smale Horseshoe Map
An important problem in the dynamics of surface homeomorphisms is determining the forcing relation between orbits. The forcing relation between periodic orbits can be computed using existing algorithms. Here we consider forcing relations between homoclinic orbits. We outline a general procedure for computing the forcing relation, and apply this to compute the equivalence and forcing relations f...
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ژورنال
عنوان ژورنال: Communications in Nonlinear Science and Numerical Simulation
سال: 2021
ISSN: ['1878-7274', '1007-5704']
DOI: https://doi.org/10.1016/j.cnsns.2020.105680