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The Resource Smooth ergodic theory for endomorphisms, Min Qian, Jian-Sheng Xie, Shu Zhu, (electronic book)

Smooth ergodic theory for endomorphisms, Min Qian, Jian-Sheng Xie, Shu Zhu, (electronic book)

Work
Publication
Extent
1 online resource (xiii, 277 p.)
Contents
  • Cover
  • Contents
  • I Preliminaries
  • I.1 Metric Entropy
  • I.2 Multiplicative Ergodic Theorem
  • I.3 Inverse Limit Space
  • II Margulis-Ruelle Inequality
  • II. 1 Statement of the Theorem
  • II. 2 Preliminaries
  • II. 3 Proof of the Theorem
  • III Expanding Maps
  • III. 1 Main Results
  • III. 2 Proof of Theorem III. 1.1
  • III. 3 Basic Facts About Expanding Maps
  • III. 4 Proofs of Theorems III. 1.2 and III. 1.3
  • IV Axiom A Endomorphisms
  • IV. 1 Introduction and Main Results
  • IV. 2 Preliminaries
  • IV. 3 Volume Lemma and the H246;lder Continuity of 966;u
  • IV. 4 Equilibrium States of 966;u on 923;f
  • IV. 5 Pesin8217;s Entropy Formula
  • IV. 6 Large Ergodic Theorem and Proof of Main Theorems
  • V Unstable and Stable Manifolds for Endomorphisms
  • V.1 Preliminary Facts
  • V.2 Fundamental Lemmas
  • V.3 Some Technical Facts About Contracting Maps
  • V.4 Local Unstable Manifolds
  • V.5 Global Unstable Sets
  • V.6 Local and Global Stable Manifolds
  • V.7 H246;lder Continuity of Sub-bundles
  • V.8 Absolute Continuity of Families of Submanifolds
  • V.9 Absolute Continuity of Conditional Measures
  • VI Pesin8217;s Entropy Formula for Endomorphisms
  • VI. 1 Main Results
  • VI. 2 Preliminaries
  • VI. 3 Proof of Theorem VI. 1.1
  • VII SRB Measures and Pesin8217;s Entropy Formula for Endomorphisms
  • VII. 1 Formulation of the SRB Property and Main Results
  • VII. 2 Technical Preparations for the Proof of the Main Result
  • VII. 3 Proof of the Sufficiency for the Entropy Formula
  • VII. 4 Lyapunov Charts
  • VII. 5 Local Unstable Manifolds and Center Unstable Sets
  • VII. 5.1 Local Unstable Manifolds and Center Unstable Sets
  • VII. 5.2 Some Estimates
  • VII. 5.3 Lipschitz Property of Unstable Subspaces within Center Unstable Sets
  • VII. 6 Related Measurable Partitions
  • VII. 6.1 Partitions Adapted to Lyapunov Charts
  • VII. 6.2 More on Increasing Partitions
  • VII. 6.3 Two Useful Partitions
  • VII. 6.4 Quotient Structure
  • VII. 6.5 Transverse Metrics
  • VII. 7 Some Consequences of Besicovitch8217;s Covering Theorem
  • VII. 8 The Main Proposition
  • VII. 9 Proof of the Necessity for the Entropy Formula
  • VII. 9.1 The Ergodic Case
  • VII. 9.2 The General Case
  • VIII Ergodic Property of Lyapunov Exponents
  • VIII. 1 Introduction and Main Results
  • VIII. 2 Lyapunov Exponents of Axiom A Attractors of Endomorphisms
  • VIII. 3 Nonuniformly Completely Hyperbolic Attractors
  • IX Generalized Entropy Formula
  • IX. 1 Related Notions and Statements of the Main Results
  • IX. 1.1 Pointwise Dimensions and Transverse Dimensions
  • IX. 1.2 Statements of the Main Results
  • IX. 2 Preliminaries
  • IX. 2.1 Some Estimations on Unstable Manifolds
  • IX. 2.2 Related Partitions
  • IX. 2.3 Transverse Metrics on i(x)/- with 2iu
  • IX. 2.4 Entropies of the Related Partitions
  • IX. 3 Definitions of Local Entropies along Unstable Manifolds
  • IX. 4 Estimates of Local Entropies along Unstable Manifolds
  • IX. 4.1 Estimate of Local Entropy h
  • IX. 4.2 Estimate of Local Entropy hi from Below with 2iu
  • IX. 4.3 Estimate of Local Entropy hi from Above with 2iu
  • IX. 5 The General Case: without Ergodic Assumption
  • X Exact Dimensionality of Hyperbolic Measures
  • X.1 Expanding Maps8217; Case8211;Proof of Theorem X.0.1
  • X.2 Diffeomorphisms8217; Case8211;Proof
Isbn
9783642019548
Instance
Label
Smooth ergodic theory for endomorphisms
Title
Smooth ergodic theory for endomorphisms
Statement of responsibility
Min Qian, Jian-Sheng Xie, Shu Zhu
Creator
Contributor
Subject
Language
eng
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorDate
1927-
http://library.link/vocab/creatorName
Qian, Min
Dewey number
515.39
Illustrations
illustrations
Index
index present
LC call number
QA313
LC item number
.Q53 2009
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1964-
http://library.link/vocab/relatedWorkOrContributorName
  • Xie, Jian-sheng
  • Zhu, Shu
Series statement
Lecture notes in mathematics,
Series volume
1978
http://library.link/vocab/subjectName
  • Ergodic theory
  • Endomorphisms (Group theory)
  • Dynamisches System
  • Théorie ergodique
  • Endomorphismes (Théorie des groupes)
Label
Smooth ergodic theory for endomorphisms, Min Qian, Jian-Sheng Xie, Shu Zhu, (electronic book)
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. 271-274) and index
Color
multicolored
Contents
Cover -- Contents -- I Preliminaries -- I.1 Metric Entropy -- I.2 Multiplicative Ergodic Theorem -- I.3 Inverse Limit Space -- II Margulis-Ruelle Inequality -- II. 1 Statement of the Theorem -- II. 2 Preliminaries -- II. 3 Proof of the Theorem -- III Expanding Maps -- III. 1 Main Results -- III. 2 Proof of Theorem III. 1.1 -- III. 3 Basic Facts About Expanding Maps -- III. 4 Proofs of Theorems III. 1.2 and III. 1.3 -- IV Axiom A Endomorphisms -- IV. 1 Introduction and Main Results -- IV. 2 Preliminaries -- IV. 3 Volume Lemma and the H246;lder Continuity of 966;u -- IV. 4 Equilibrium States of 966;u on 923;f -- IV. 5 Pesin8217;s Entropy Formula -- IV. 6 Large Ergodic Theorem and Proof of Main Theorems -- V Unstable and Stable Manifolds for Endomorphisms -- V.1 Preliminary Facts -- V.2 Fundamental Lemmas -- V.3 Some Technical Facts About Contracting Maps -- V.4 Local Unstable Manifolds -- V.5 Global Unstable Sets -- V.6 Local and Global Stable Manifolds -- V.7 H246;lder Continuity of Sub-bundles -- V.8 Absolute Continuity of Families of Submanifolds -- V.9 Absolute Continuity of Conditional Measures -- VI Pesin8217;s Entropy Formula for Endomorphisms -- VI. 1 Main Results -- VI. 2 Preliminaries -- VI. 3 Proof of Theorem VI. 1.1 -- VII SRB Measures and Pesin8217;s Entropy Formula for Endomorphisms -- VII. 1 Formulation of the SRB Property and Main Results -- VII. 2 Technical Preparations for the Proof of the Main Result -- VII. 3 Proof of the Sufficiency for the Entropy Formula -- VII. 4 Lyapunov Charts -- VII. 5 Local Unstable Manifolds and Center Unstable Sets -- VII. 5.1 Local Unstable Manifolds and Center Unstable Sets -- VII. 5.2 Some Estimates -- VII. 5.3 Lipschitz Property of Unstable Subspaces within Center Unstable Sets -- VII. 6 Related Measurable Partitions -- VII. 6.1 Partitions Adapted to Lyapunov Charts -- VII. 6.2 More on Increasing Partitions -- VII. 6.3 Two Useful Partitions -- VII. 6.4 Quotient Structure -- VII. 6.5 Transverse Metrics -- VII. 7 Some Consequences of Besicovitch8217;s Covering Theorem -- VII. 8 The Main Proposition -- VII. 9 Proof of the Necessity for the Entropy Formula -- VII. 9.1 The Ergodic Case -- VII. 9.2 The General Case -- VIII Ergodic Property of Lyapunov Exponents -- VIII. 1 Introduction and Main Results -- VIII. 2 Lyapunov Exponents of Axiom A Attractors of Endomorphisms -- VIII. 3 Nonuniformly Completely Hyperbolic Attractors -- IX Generalized Entropy Formula -- IX. 1 Related Notions and Statements of the Main Results -- IX. 1.1 Pointwise Dimensions and Transverse Dimensions -- IX. 1.2 Statements of the Main Results -- IX. 2 Preliminaries -- IX. 2.1 Some Estimations on Unstable Manifolds -- IX. 2.2 Related Partitions -- IX. 2.3 Transverse Metrics on i(x)/- with 2iu -- IX. 2.4 Entropies of the Related Partitions -- IX. 3 Definitions of Local Entropies along Unstable Manifolds -- IX. 4 Estimates of Local Entropies along Unstable Manifolds -- IX. 4.1 Estimate of Local Entropy h -- IX. 4.2 Estimate of Local Entropy hi from Below with 2iu -- IX. 4.3 Estimate of Local Entropy hi from Above with 2iu -- IX. 5 The General Case: without Ergodic Assumption -- X Exact Dimensionality of Hyperbolic Measures -- X.1 Expanding Maps8217; Case8211;Proof of Theorem X.0.1 -- X.2 Diffeomorphisms8217; Case8211;Proof
Control code
SPR656399529
Dimensions
unknown
Extent
1 online resource (xiii, 277 p.)
Form of item
online
Isbn
9783642019548
Other control number
9786612655807
Other physical details
ill.
Specific material designation
remote
Label
Smooth ergodic theory for endomorphisms, Min Qian, Jian-Sheng Xie, Shu Zhu, (electronic book)
Publication
Bibliography note
Includes bibliographical references (p. 271-274) and index
Color
multicolored
Contents
Cover -- Contents -- I Preliminaries -- I.1 Metric Entropy -- I.2 Multiplicative Ergodic Theorem -- I.3 Inverse Limit Space -- II Margulis-Ruelle Inequality -- II. 1 Statement of the Theorem -- II. 2 Preliminaries -- II. 3 Proof of the Theorem -- III Expanding Maps -- III. 1 Main Results -- III. 2 Proof of Theorem III. 1.1 -- III. 3 Basic Facts About Expanding Maps -- III. 4 Proofs of Theorems III. 1.2 and III. 1.3 -- IV Axiom A Endomorphisms -- IV. 1 Introduction and Main Results -- IV. 2 Preliminaries -- IV. 3 Volume Lemma and the H246;lder Continuity of 966;u -- IV. 4 Equilibrium States of 966;u on 923;f -- IV. 5 Pesin8217;s Entropy Formula -- IV. 6 Large Ergodic Theorem and Proof of Main Theorems -- V Unstable and Stable Manifolds for Endomorphisms -- V.1 Preliminary Facts -- V.2 Fundamental Lemmas -- V.3 Some Technical Facts About Contracting Maps -- V.4 Local Unstable Manifolds -- V.5 Global Unstable Sets -- V.6 Local and Global Stable Manifolds -- V.7 H246;lder Continuity of Sub-bundles -- V.8 Absolute Continuity of Families of Submanifolds -- V.9 Absolute Continuity of Conditional Measures -- VI Pesin8217;s Entropy Formula for Endomorphisms -- VI. 1 Main Results -- VI. 2 Preliminaries -- VI. 3 Proof of Theorem VI. 1.1 -- VII SRB Measures and Pesin8217;s Entropy Formula for Endomorphisms -- VII. 1 Formulation of the SRB Property and Main Results -- VII. 2 Technical Preparations for the Proof of the Main Result -- VII. 3 Proof of the Sufficiency for the Entropy Formula -- VII. 4 Lyapunov Charts -- VII. 5 Local Unstable Manifolds and Center Unstable Sets -- VII. 5.1 Local Unstable Manifolds and Center Unstable Sets -- VII. 5.2 Some Estimates -- VII. 5.3 Lipschitz Property of Unstable Subspaces within Center Unstable Sets -- VII. 6 Related Measurable Partitions -- VII. 6.1 Partitions Adapted to Lyapunov Charts -- VII. 6.2 More on Increasing Partitions -- VII. 6.3 Two Useful Partitions -- VII. 6.4 Quotient Structure -- VII. 6.5 Transverse Metrics -- VII. 7 Some Consequences of Besicovitch8217;s Covering Theorem -- VII. 8 The Main Proposition -- VII. 9 Proof of the Necessity for the Entropy Formula -- VII. 9.1 The Ergodic Case -- VII. 9.2 The General Case -- VIII Ergodic Property of Lyapunov Exponents -- VIII. 1 Introduction and Main Results -- VIII. 2 Lyapunov Exponents of Axiom A Attractors of Endomorphisms -- VIII. 3 Nonuniformly Completely Hyperbolic Attractors -- IX Generalized Entropy Formula -- IX. 1 Related Notions and Statements of the Main Results -- IX. 1.1 Pointwise Dimensions and Transverse Dimensions -- IX. 1.2 Statements of the Main Results -- IX. 2 Preliminaries -- IX. 2.1 Some Estimations on Unstable Manifolds -- IX. 2.2 Related Partitions -- IX. 2.3 Transverse Metrics on i(x)/- with 2iu -- IX. 2.4 Entropies of the Related Partitions -- IX. 3 Definitions of Local Entropies along Unstable Manifolds -- IX. 4 Estimates of Local Entropies along Unstable Manifolds -- IX. 4.1 Estimate of Local Entropy h -- IX. 4.2 Estimate of Local Entropy hi from Below with 2iu -- IX. 4.3 Estimate of Local Entropy hi from Above with 2iu -- IX. 5 The General Case: without Ergodic Assumption -- X Exact Dimensionality of Hyperbolic Measures -- X.1 Expanding Maps8217; Case8211;Proof of Theorem X.0.1 -- X.2 Diffeomorphisms8217; Case8211;Proof
Control code
SPR656399529
Dimensions
unknown
Extent
1 online resource (xiii, 277 p.)
Form of item
online
Isbn
9783642019548
Other control number
9786612655807
Other physical details
ill.
Specific material designation
remote

Subject

Member of

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