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The Resource Smooth Ergodic Theory for Endomorphisms, by Min Qian, Jian-Sheng Xie, Shu Zhu, (electronic resource)

Smooth Ergodic Theory for Endomorphisms, by Min Qian, Jian-Sheng Xie, Shu Zhu, (electronic resource)

Creator
Author
Contributor
Summary
This volume presents a general smooth ergodic theory for deterministic dynamical systems generated by non-invertible endomorphisms, mainly concerning the relations between entropy, Lyapunov exponents and dimensions. The authors make extensive use of the combination of the inverse limit space technique and the techniques developed to tackle random dynamical systems. The most interesting results in this book are (1) the equivalence between the SRB property and Pesin’s entropy formula; (2) the generalized Ledrappier-Young entropy formula; (3) exact-dimensionality for weakly hyperbolic diffeomorphisms and for expanding maps. The proof of the exact-dimensionality for weakly hyperbolic diffeomorphisms seems more accessible than that of Barreira et al. It also inspires the authors to argue to what extent the famous Eckmann-Ruelle conjecture and many other classical results for diffeomorphisms and for flows hold true. After a careful reading of the book, one can systematically learn the Pesin theory for endomorphisms as well as the typical tricks played in the estimation of the number of balls of certain properties, which are extensively used in Chapters IX and X
Language
eng
Work
Publication
Contents
  • Preliminaries
  • Margulis-Ruelle Inequality
  • Expanding Maps
  • Axiom A Endomorphisms
  • Unstable and Stable Manifolds for Endomorphisms
  • Pesin’s Entropy Formula for Endomorphisms
  • SRB Measures and Pesin’s Entropy Formula for Endomorphisms
  • Ergodic Property of Lyapunov Exponents
  • Generalized Entropy Formula
  • Exact Dimensionality of Hyperbolic Measures
Isbn
9783642019548
Instance
Label
Smooth Ergodic Theory for Endomorphisms
Title
Smooth Ergodic Theory for Endomorphisms
Statement of responsibility
by Min Qian, Jian-Sheng Xie, Shu Zhu
Creator
Contributor
Author
Provider
Subject
Language
eng
Summary
This volume presents a general smooth ergodic theory for deterministic dynamical systems generated by non-invertible endomorphisms, mainly concerning the relations between entropy, Lyapunov exponents and dimensions. The authors make extensive use of the combination of the inverse limit space technique and the techniques developed to tackle random dynamical systems. The most interesting results in this book are (1) the equivalence between the SRB property and Pesin’s entropy formula; (2) the generalized Ledrappier-Young entropy formula; (3) exact-dimensionality for weakly hyperbolic diffeomorphisms and for expanding maps. The proof of the exact-dimensionality for weakly hyperbolic diffeomorphisms seems more accessible than that of Barreira et al. It also inspires the authors to argue to what extent the famous Eckmann-Ruelle conjecture and many other classical results for diffeomorphisms and for flows hold true. After a careful reading of the book, one can systematically learn the Pesin theory for endomorphisms as well as the typical tricks played in the estimation of the number of balls of certain properties, which are extensively used in Chapters IX and X
Member of
http://library.link/vocab/creatorName
Qian, Min
Image bit depth
0
LC call number
QA313
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
  • Xie, Jian-Sheng.
  • Zhu, Shu.
  • SpringerLink
Series statement
Lecture Notes in Mathematics,
Series volume
1978
http://library.link/vocab/subjectName
  • Mathematics
  • Differentiable dynamical systems
  • Mechanical engineering
  • Mathematics
  • Dynamical Systems and Ergodic Theory
  • Mechanical Engineering
Label
Smooth Ergodic Theory for Endomorphisms, by Min Qian, Jian-Sheng Xie, Shu Zhu, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preliminaries -- Margulis-Ruelle Inequality -- Expanding Maps -- Axiom A Endomorphisms -- Unstable and Stable Manifolds for Endomorphisms -- Pesin’s Entropy Formula for Endomorphisms -- SRB Measures and Pesin’s Entropy Formula for Endomorphisms -- Ergodic Property of Lyapunov Exponents -- Generalized Entropy Formula -- Exact Dimensionality of Hyperbolic Measures
Dimensions
unknown
File format
multiple file formats
Form of item
electronic
Isbn
9783642019548
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-642-01954-8
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-642-01954-8
Label
Smooth Ergodic Theory for Endomorphisms, by Min Qian, Jian-Sheng Xie, Shu Zhu, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preliminaries -- Margulis-Ruelle Inequality -- Expanding Maps -- Axiom A Endomorphisms -- Unstable and Stable Manifolds for Endomorphisms -- Pesin’s Entropy Formula for Endomorphisms -- SRB Measures and Pesin’s Entropy Formula for Endomorphisms -- Ergodic Property of Lyapunov Exponents -- Generalized Entropy Formula -- Exact Dimensionality of Hyperbolic Measures
Dimensions
unknown
File format
multiple file formats
Form of item
electronic
Isbn
9783642019548
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-642-01954-8
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-642-01954-8

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