Titlebook: Lyapunov Exponents; Luís Barreira Book 2017 Springer International Publishing AG 2017 regularity.hyperbolicity.ergodic theory.multifractal

拱墙

Lyapunov Exponents and Regularityarity in terms of the Grobman coefficient. This is part of what is usually called the abstract theory of Lyapunov exponents. We then illustrate the notions with two specific classes of Lyapunov exponents obtained from a linear dynamics. More precisely, we consider linear dynamics with discrete and c

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JUST

Preservation of Lyapunov Exponentsyapunov exponent unchanged. In particular, we show that a sequence of invertible matrices can be reduced to a sequence of block matrices with upper-triangular blocks if and only if the space can be decomposed into an invariant splitting such that the angles between complementary invariant subspaces

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Singular Valuesil the relation between singular values and Lyapunov exponents, both for discrete and continuous time. We first show that the general inequalities between the values of the Lyapunov exponent and of the upper exponential growth rates of the singular values are the best possible. More precisely, we sh

焦虑

Characterizations of Regularityl growth rates of the singular values and in terms of a certain symmetrized version of the dynamics. We consider both discrete and continuous time. Moreover, for a sequence of matrices, we introduce a third regularity coefficient—the Lyapunov coefficient—and we relate it to the Grobman and Perron co

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Tempered Dichotomiesistence of a nonzero Lyapunov exponent gives rise to hyperbolicity and how this relates to the theory of regularity. We start with the simpler case of sequences of matrices with a negative Lyapunov exponent, for which the exposition is simpler. We also consider the notion of strong tempered spectrum

原谅

Lyapunov Sequenceswith the simpler case of a tempered dichotomy, we show in this case that the notion can be completely characterized in terms of the existence of a strict quadratic Lyapunov sequence. This includes explicitly constructing such a sequence for any tempered dichotomy. The chapter can be considered as a

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Cocycles and Lyapunov Exponentsbased on the results on singular values established in Chap. . combined with the subadditive ergodic theorem. We also show how a nonvanishing Lyapunov exponent for a cocycle gives rise to nonuniform hyperbolicity. In particular, the structure that the theorem determines is fundamental in many develo

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