Rigorous numerical approximation of escape rates
نویسندگان
چکیده
منابع مشابه
Rigorous Shadowing of Numerical
Rigorous Shadowing of Numerical Solutions of Ordinary Di erential Equations by Containment Wayne Brian Hayes Doctor of Philosophy Graduate Department of Computer Science University of Toronto 2001 An exact trajectory of a dynamical system lying close to a numerical trajectory is called a shadow. We present a general-purpose method for proving the existence of nite-time shadows of numerical ODE ...
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An exact trajectory of a dynamical system lying close to a numerical trajectory is called a shadow. We present a general-purpose method for proving the existence of nite-time shadows of numerical ODE integrations of arbitrary dimension in which some measure of hyperbolicity is present and there is either 0 or 1 expanding modes, or 0 or 1 contracting modes. Much of the rigor is provided automati...
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It is well known that for different classes of transformations, including the class of piecewise C expanding maps T : [0, 1] , Ulam’s method is an efficient way to numerically approximate the absolutely continuous invariant measure of T . We develop a new extension of Ulam’s method and prove that this extension can be used for the numerical approximation of the Ruelle-PerronFrobenius operator a...
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Consider a C 1+ diieomorphism f having a uniformly hyperbolic compact invariant set , maximal invariant in some small neighbourhood of itself. The asymp-totic exponential rate of escape from any small enough neighbourhood of is given by the topological pressure of ? log jJ u fj on (Bowen{Ruelle 1975]). It has been conjectured (Eckmann{Ruelle 1985]) that this property, formulated in terms of esc...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2006
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/19/11/002