http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
finite dimensional deterministic studies
Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.
1 online resource (xi, 309 pages) : illustrations
The study of non-linear dynamical systems nowadays is an intricate mixture of analysis, geometry, algebra and measure theory and this book takes all aspects into account. Presenting the contents of its authors' graduate courses in non-linear dynamical systems, this volume aims at researchers who wish to be acquainted with the more theoretical and fundamental subjects in non-linear dynamics and is designed to link the popular literature with research papers and monographs. All of the subjects covered in this book are extensively dealt with and presented in a pedagogic form. These include the presentation of an environment for the route to chaos by quasi-periodicity (which is related to the Landau-Lifschitz and Ruelle-Takens scenario's concerning the onset of turbulence); the theories of 1-dimensional dynamics, singularities in planar vector fields, and quasi-periodicity in dissipative systems.
Front Cover; Structures in Dynamics: Finite Dimensional Deterministic Studies; Copyright Page; Preface; Table of Contents; Chapter 1. Introduction to dynamical systems; 1.1 What is a dynamical system?; 1.2 Setting of the problem; 1.3 References; Chapter 2. Genericity and structural stability; 2.1 Persistence, topology; 2.2 Equivalent dynamics, structural stability; 2.3 Is structural stability a generic property?; 2.4 Miscellaneous remarks; 2.5 Vector fields on compact surfaces; 2.6 References; Chapter 3. Bifurcations; 3.1 The saddle node bifurcation; 3.2 The period doubling bifurcation
3.3 The Hopf bifurcation3.4 Final remarks; 3.5 References; Chapter 4. A family of quasi-periodic attractors; 4.1 Definition of quasi-periodicity, setting of the problem; 4.2 Two examples, a preliminary perturbation analysis; 4.3 The perturbation problem for circle maps; 4.4 Some conservative remarks; 4.5 References; Chapter 5. Chaos; 5.1 Time series; 5.2 Prediction procedure; 5.3 Interpretation of dimension and entropy for dynamical systems; 5.4 On the definition of chaos; 5.5 Chaos: probabilistic aspects; 5.6 References; Chapter 6. Interval maps; 6.1 Combinatorics of interval maps
6.2 Topological properties of interval maps6.3 Metric and statistical results; 6.4 Some final remarks; 6.5 References; Chapter 7. Local study of planar vector fields: singularities and their unfoldings; 7.1 Introduction; 7.2 Study of the singularities; 7.3 Versal unfoldings for singularities of vector fields; 7.4 Reduction to the centre manifold; 7.5 Blowing up; 7.6 Normal forms; 7.7 C°°-unfoldings on R and semi-hyperbolic bifurcations on R2; 7.8 Hopf-Takens bifurcations on R2; 7.9 Some global bifurcations of codimension 1 on the plane; 7.10 The Bogdanov-Takens bifurcation; 7.11 References
Chapter 8. The thermodynamic formalism8.1 Invariant measures for dynamical systems; 8.2 Measures describing thermodynamic states; 8.3 The Ruelle operator; 8.4 References; Chapter 9. Conservative dynamical systems; 9.1 Introduction; 9.2 Examples of integrable systems; 9.3 Hamiltonian systems; 9.4 Integrable systems; 9.5 Near integrability; 9.6 References; Subject index
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Includes bibliographical references and index.
Amsterdam : North-Holland ; New York, N.Y. : Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., ©1991