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The aim of this monograph is to present a general method of proving
continuity of Lyapunov exponents of linear cocycles. The method
uses an inductive procedure based on a general, geometric version
of the Avalanche Principle. The main assumption required by this
method is the availability of appropriate large deviation type
estimates for quantities related to the iterates of the base and
fiber dynamics associated with the linear cocycle. We establish
such estimates for various models of random and quasi-periodic
cocycles. Our method has its origins in a paper of M. Goldstein and
W. Schlag. Our present work expands upon their approach in both
depth and breadth. We conclude this monograph with a list of
related open problems, some of which may be treated using a similar
approach.
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New Trends in Lyapunov Exponents - NTLE, Lisbon, Portugal, February 7–11, 2022 (1st ed. 2023)
João Lopes Dias, Pedro Duarte, José Pedro Gaivão, Silvius Klein, Telmo Peixe, …
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R5,210
Discovery Miles 52 100
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Ships in 10 - 15 working days
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This volume presents peer-reviewed surveys on new developments in
the study of Lyapunov exponents in dynamical systems and its
applications to other areas, such as mathematical physics. Written
by leading experts in their fields, the contributions are based
upon the presentations given by invited speakers at the “New
Trends in Lyapunov Exponents” workshop held in Lisbon, Portugal,
February 7–11, 2022. The works focus on the concept of Lyapunov
exponents in their various manifestations in dynamical systems
along with their applications to mathematical physics and other
areas of mathematics. The papers reflect the spirit of the
conference of promoting new connections among different subjects in
dynamical systems. This volume aims primarily at researchers and
graduate students working in dynamical systems and related fields,
serving as an introduction to active fields of research and as a
review of recent results as well.
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