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Erschienen in:
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2015 | OriginalPaper | Buchkapitel

A Note on the Large Deviations for Piecewise Expanding Multidimensional Maps

verfasst von : R. Aimino, S. Vaienti

Erschienen in: Nonlinear Dynamics New Directions

Verlag: Springer International Publishing

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Abstract

We present here the large deviation principle for some systems admitting a spectral gap, by using the functional approach of Hennion and Hervé, with slight modification. Our main application concerns multidimensional expanding maps introduced by Saussol.

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Nächstes Kapitel Directional Metric Entropy and Lyapunov Exponents for Dynamical Systems Generated by Cellular Automata
Fußnoten
1
When \(\varphi \in{\cal B}^{\star}\) belongs to the topological dual of \({\cal B}\), we denote \(<\varphi, f> = \varphi(f)\). The linear form \(f \to \int f \, dm\) belongs to \({\cal B}^{\star}\), and we denote it by m.
 
2
See corollaries III.11 and III.6 in [17].
 
3
By checking the proof, we only need that \({\cal B}\) is a Banach algebra and \(\phi \in{\cal B}\) to prove that the operators P z are well defined and holomorphic in z. So we can just assume that ϕ is such that P z define a holomorphic family of bounded operators on \({\cal B}\) for z in a complex neighborhood of 0, with successive derivatives at 0 given by C n .
 
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Metadaten
Titel
A Note on the Large Deviations for Piecewise Expanding Multidimensional Maps
verfasst von
R. Aimino
S. Vaienti
Copyright-Jahr
2015
Buch
Nonlinear Dynamics New Directions

Print ISBN: 978-3-319-09866-1

Electronic ISBN: 978-3-319-09867-8

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-3-319-09867-8_1

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