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Yes, there is such a theory, and you already gave yourself the answer in the tag. For particular shape of your map $S$, i.e. a linear hyperbolic map (meaning: the spectrum is disjoint from the unit circle) $T$ plus a small (in a sense to be precised) Lipschitz perturbation , the [Hartman-Grobman][1] tells you that $S$ is conjugated with $T$ by a Hölder continuous homeomorphism. The proof is very elementary and follows from the contraction principle; see e.g. M.Shub's book, Global stability of Dynamical Systems. [1]:http://en.wikipedia.org/wiki/Hartman%E2%80%93Grobman_theorem

Yes, there is such a theory, and you already gave yourself the answer in the tag. For particular shape of your map $S$, i.e. a linear hyperbolic map (meaning: the spectrum is disjoint from the unit circle) $T$ plus a small (in a sense to be precised) Lipschitz perturbation , the Hartman-Grobman tells you that $S$ is conjugated with $T$ by a Hölder continuous homeomorphism. The proof is very elementary and follows from the contraction principle; see e.g. M.Shub's book, Global stability of Dynamical Systems.

Yes, there is such a theory, and you already gave yourself the answer in the tag! For particular shape of your map $S$, i.e. a linear hyperbolic map (meaning: the spectrum is disjoint from the unit circle) $T$ plus a small (in a sense to be precised) Lipschitz perturbation , the [Hartman-Grobman][1] tells you that $S$ is conjugated with $T$ by a Hölder continuous homeomorphism. The proof is very elementary and follows from the contraction principle; see e.g. M.Shub's book, Global stability of Dynamical Systems. [1]:http://en.wikipedia.org/wiki/Hartman%E2%80%93Grobman_theorem

Yes, there is such a theory, and you already gave yourself the answer in the tag. For particular shape of your map $S$, i.e. a linear hyperbolic map (meaning: the spectrum is disjoint from the unit circle) $T$ plus a small (in a sense to be precised) Lipschitz perturbation , the [Hartman-Grobman][1] tells you that $S$ is conjugated with $T$ by a Hölder continuous homeomorphism. The proof is very elementary and follows from the contraction principle; see e.g. M.Shub's book, Global stability of Dynamical Systems. [1]:http://en.wikipedia.org/wiki/Hartman%E2%80%93Grobman_theorem

Yes, there is such a theory, and you already gave yourself the answer in the tag! For particular shape of your map $S$, i.e. a linear hyperbolic map (meaning: the spectrum is disjoint from the unit circle) $T$ plus a small (in a sense to be precised) Lipschitz perturbation , the [Hartman-Grobman][1] tells you that $S$ is conjugated with $T$ by a Hoelder continuous homeomorphism. [1]:http://en.wikipedia.org/wiki/Hartman%E2%80%93Grobman_theorem

Yes, there is such a theory, and you already gave yourself the answer in the tag! For particular shape of your map $S$, i.e. a linear hyperbolic map (meaning: the spectrum is disjoint from the unit circle) $T$ plus a small (in a sense to be precised) Lipschitz perturbation , the [Hartman-Grobman][1] tells you that $S$ is conjugated with $T$ by a Hölder continuous homeomorphism. The proof is very elementary and follows from the contraction principle; see e.g. M.Shub's book, Global stability of Dynamical Systems. [1]:http://en.wikipedia.org/wiki/Hartman%E2%80%93Grobman_theorem