Fourier–Taylor Approximation of Unstable Manifolds for Compact Maps: Numerical Implementation and Computer-Assisted Error Bounds
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DOI: 10.1007/s10208-016-9325-9
Abstract: We develop and implement a semi-numerical method for computing high-order Taylor approximations of unstable manifolds for hyperbolic fixed points of compact infinite-dimensional maps. The method can follow folds in the embedding and describes precisely the… read more here.
Keywords: error bounds; computer assisted; unstable manifolds; taylor approximation ... See more keywords
Linear response theory for diffeomorphisms with tangencies of stable and unstable manifolds—a contribution to the Gallavotti–Cohen chaotic hypothesis
Sign Up to like & getrecommendations! Published in 2018 at "Nonlinearity"
DOI: 10.1088/1361-6544/aae740
Abstract: This note presents a non-rigorous study of the linear response for an SRB (or `natural physical') measure $\rho$ of a diffeomorphism $f$ in the presence of tangencies of the stable and unstable manifolds of $\rho$.… read more here.
Keywords: response theory; linear response; unstable manifolds; stable unstable ... See more keywords