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The Resource Smooth Ergodic Theory for Endomorphisms, by Min Qian, JianSheng Xie, Shu Zhu, (electronic resource)
Smooth Ergodic Theory for Endomorphisms, by Min Qian, JianSheng Xie, Shu Zhu, (electronic resource)
Resource Information
The item Smooth Ergodic Theory for Endomorphisms, by Min Qian, JianSheng Xie, Shu Zhu, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Smooth Ergodic Theory for Endomorphisms, by Min Qian, JianSheng Xie, Shu Zhu, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 This volume presents a general smooth ergodic theory for deterministic dynamical systems generated by noninvertible 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 LedrappierYoung entropy formula; (3) exactdimensionality for weakly hyperbolic diffeomorphisms and for expanding maps. The proof of the exactdimensionality 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 EckmannRuelle 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
 Contents

 Preliminaries
 MargulisRuelle 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
 Label
 Smooth Ergodic Theory for Endomorphisms
 Title
 Smooth Ergodic Theory for Endomorphisms
 Statement of responsibility
 by Min Qian, JianSheng Xie, Shu Zhu
 Language
 eng
 Summary
 This volume presents a general smooth ergodic theory for deterministic dynamical systems generated by noninvertible 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 LedrappierYoung entropy formula; (3) exactdimensionality for weakly hyperbolic diffeomorphisms and for expanding maps. The proof of the exactdimensionality 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 EckmannRuelle 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
 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, JianSheng.
 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, JianSheng Xie, Shu Zhu, (electronic resource)
 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  MargulisRuelle 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
 10.1007/9783642019548
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783642019548
 Label
 Smooth Ergodic Theory for Endomorphisms, by Min Qian, JianSheng Xie, Shu Zhu, (electronic resource)
 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  MargulisRuelle 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
 10.1007/9783642019548
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783642019548
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.bu.edu/portal/SmoothErgodicTheoryforEndomorphismsbyMin/0CgVZb2A2AI/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.bu.edu/portal/SmoothErgodicTheoryforEndomorphismsbyMin/0CgVZb2A2AI/">Smooth Ergodic Theory for Endomorphisms, by Min Qian, JianSheng Xie, Shu Zhu, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.bu.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.bu.edu/">Boston University Libraries</a></span></span></span></span></div>