Data Portal @ linkeddatafragments.org

Matches in Harvard for { <http://id.lib.harvard.edu/aleph/008766254/catalog> ?p ?o. }

• catalog abstract ""This book is a systematic introduction to smooth ergodic theory. The topics discussed include the general (abstract) theory of Lyapunov exponents and its applications to the stability theory of differential equations, stable manifold theory, absolute continuity, and the ergodic theory of dynamical systems with nonzero Lyapunov exponents (including geodesic flows)." "The authors consider several nontrivial examples of dynamical systems with nonzero Lyapunov exponents to illustrate some basic methods and ideas of the theory." "This book is self-contained. The reader needs a basic knowledge of real analysis, measure theory, differential equations, and topology. The authors present basic concepts of smooth ergodic theory and provide complete proofs of the main results. They also state some more advanced results to give readers a broader view of smooth ergodic theory. This volume may be used by those nonexperts who wish to become familiar with the field."--Jacket.".
• catalog contributor b12286355.
• catalog contributor b12286356.
• catalog created "c2002.".
• catalog date "2002".
• catalog date "c2002.".
• catalog dateCopyrighted "c2002.".
• catalog description ""This book is a systematic introduction to smooth ergodic theory. The topics discussed include the general (abstract) theory of Lyapunov exponents and its applications to the stability theory of differential equations, stable manifold theory, absolute continuity, and the ergodic theory of dynamical systems with nonzero Lyapunov exponents (including geodesic flows)." "The authors consider several nontrivial examples of dynamical systems with nonzero Lyapunov exponents to illustrate some basic methods and ideas of the theory." "This book is self-contained. The reader needs a basic knowledge of real analysis, measure theory, differential equations, and topology. The authors present basic concepts of smooth ergodic theory and provide complete proofs of the main results. They also state some more advanced results to give readers a broader view of smooth ergodic theory. This volume may be used by those nonexperts who wish to become familiar with the field."--Jacket.".
• catalog description "Ch. 1. Lyapunov Stability Theory of Differential Equations -- 1.1. Lyapunov Exponents for Differential Equations -- 1.2. Abstract Theory of Lyapunov Exponents -- 1.3. Forward and Backward Regularity -- 1.4. Stability Theory of Nonautonomous Differential Equations -- 1.5. Lyapunov Regularity and the Oseledets Decomposition -- Ch. 2. Elements of Nonuniform Hyperbolic Theory -- 2.1. Dynamical Systems with Nonzero Lyapunov Exponents -- 2.2. Nonuniform Hyperbolicity and Regular Sets -- 2.3. Holder Continuity of Invariant Distributions -- 2.4. Proof of the Multiplicative Ergodic Theorem -- Ch. 3. Examples of Nonuniformly Hyperbolic Systems -- 3.1. Anosov Diffeomorphisms -- 3.2. Diffeomorphisms with Nonzero Lyapunov Exponents on Surfaces -- 3.3. A Flow with Nonzero Lyapunov Exponents -- 3.4. Geodesic Flows on Compact Manifolds of Nonpositive Curvature -- Ch. 4. Local Manifold Theory -- 4.1. Existence of Local Stable Manifolds -- 4.2. Basic Properties of Stable and Unstable Manifolds -- 4.3. Absolute Continuity Property -- 4.4. Computing the Jacobian of the Holonomy Map -- 4.5. Partial Hyperbolicity -- Ch. 5. Ergodic Properties of Smooth Hyperbolic Measures -- 5.1. Absolute Continuity and Smooth Invariant Measures -- 5.2. Ergodicity of Smooth Hyperbolic Measures -- 5.3. Local Ergodicity -- 5.4. The Entropy Formula -- 5.5. SRB-Measures and General Hyperbolic Measures -- 5.6. Geodesic Flows on Compact Surfaces of Nonpositive Curvature.".
• catalog description "Includes bibliographical references (p. 145-146) and index.".
• catalog extent "xi, 151 p. :".
• catalog identifier "0821829211 (alk. paper)".
• catalog isPartOf "University lecture series (Providence, R.I.) ; 23.".
• catalog isPartOf "University lecture series, 1047-3998 ; v. 23".
• catalog issued "2002".
• catalog issued "c2002.".
• catalog language "eng".
• catalog publisher "Providence, RI : American Mathematical Society,".
• catalog subject "515/.42 21".
• catalog subject "Ergodic theory.".
• catalog subject "Lyapunov exponents.".
• catalog subject "QA611.5 .B37 2002".
• catalog tableOfContents "Ch. 1. Lyapunov Stability Theory of Differential Equations -- 1.1. Lyapunov Exponents for Differential Equations -- 1.2. Abstract Theory of Lyapunov Exponents -- 1.3. Forward and Backward Regularity -- 1.4. Stability Theory of Nonautonomous Differential Equations -- 1.5. Lyapunov Regularity and the Oseledets Decomposition -- Ch. 2. Elements of Nonuniform Hyperbolic Theory -- 2.1. Dynamical Systems with Nonzero Lyapunov Exponents -- 2.2. Nonuniform Hyperbolicity and Regular Sets -- 2.3. Holder Continuity of Invariant Distributions -- 2.4. Proof of the Multiplicative Ergodic Theorem -- Ch. 3. Examples of Nonuniformly Hyperbolic Systems -- 3.1. Anosov Diffeomorphisms -- 3.2. Diffeomorphisms with Nonzero Lyapunov Exponents on Surfaces -- 3.3. A Flow with Nonzero Lyapunov Exponents -- 3.4. Geodesic Flows on Compact Manifolds of Nonpositive Curvature -- Ch. 4. Local Manifold Theory -- 4.1. Existence of Local Stable Manifolds -- 4.2. Basic Properties of Stable and Unstable Manifolds -- 4.3. Absolute Continuity Property -- 4.4. Computing the Jacobian of the Holonomy Map -- 4.5. Partial Hyperbolicity -- Ch. 5. Ergodic Properties of Smooth Hyperbolic Measures -- 5.1. Absolute Continuity and Smooth Invariant Measures -- 5.2. Ergodicity of Smooth Hyperbolic Measures -- 5.3. Local Ergodicity -- 5.4. The Entropy Formula -- 5.5. SRB-Measures and General Hyperbolic Measures -- 5.6. Geodesic Flows on Compact Surfaces of Nonpositive Curvature.".
• catalog title "Lyapunov exponents and smooth ergodic theory / Luis Barreira and Yakov B. Pesin.".
• catalog type "text".