MARC details
| 000 -LEADER |
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| fixed length control field |
05054nmm a22002535i 4500 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20230705150649.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
121227s1993 gw | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783642780431 |
| -- |
978-3-642-78043-1 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
515.8 |
| Edition number |
23 |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Melo, Welington de. |
| 9 (RLIN) |
21102 |
| 245 ## - TITLE STATEMENT |
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| Title |
One-Dimensional Dynamics |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc. |
by Welington de Melo, Sebastian van Strien. |
| 250 ## - EDITION STATEMENT |
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| Edition statement |
1st ed. 1993. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. |
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| Place of publication, distribution, etc. |
Berlin, Heidelberg : |
| Name of publisher, distributor, etc. |
Springer Berlin Heidelberg : |
| -- |
Imprint: Springer, |
| Date of publication, distribution, etc. |
1993. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
XIV, 606 p. |
| Other physical details |
online resource. |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
0. Introduction -- I. Circle Diffeomorphisms -- 1. The Combinatorial Theory of Poincaré -- 2. The Topological Theory of Denjoy -- 3. Smooth Conjugacy Results -- 4. Families of Circle Diffeomorphisms; Arnol'd tongues -- 5. Counter-Examples to Smooth Linearizability -- 6. Frequency of Smooth Linearizability in Families -- 7. Some Historical Comments and Further Remarks -- II. The Combinatorics of One-Dimensional Endomorphisms -- 1. The Theorem of Sarkovskii -- 2. Covering Maps of the Circle as Dynamical Systems -- 3. The Kneading Theory and Combinatorial Equivalence -- 4. Full Families and Realization of Maps -- 5. Families of Maps and Renormalization -- 6. Piecewise Monotone Maps can be Modelled by Polynomial Maps -- 7. The Topological Entropy -- 8. The Piecewise Linear Model -- 9. Continuity of the Topological Entropy -- 10. Monotonicity of the Kneading Invariant for the Quadratic Family -- 11. Some Historical Comments and Further Remarks -- III. Structural Stability and Hyperbolicity -- 1. The Dynamics of Rational Mappings -- 2. Structural Stability and Hyperbolicity -- 3. Hyperbolicity in Maps with Negative Schwarzian Derivative -- 4. The Structure of the Non-Wandering Set -- 5. Hyperbolicity in Smooth Maps -- 6. Misiurewicz Maps are Almost Hyperbolic -- 7. Some Further Remarks and Open Questions -- IV. The Structure of Smooth Maps -- 1. The Cross-Ratio: the Minimum and Koebe Principle -- 2. Distortion of Cross-Ratios -- 3. Koebe Principles on Iterates -- 4. Some Simplifications and the Induction Assumption -- 5. The Pullback of Space: the Koebe/Contraction Principle -- 6. Disjointness of Orbits of Intervals -- 7. Wandering Intervals Accumulate on Turning Points -- 8. Topological Properties of a Unimodal Pullback -- 9. The Non-Existence of Wandering Intervals -- 10. Finiteness of Attractors -- 11. Some Further Remarks and Open Questions -- V. Ergodic Properties and Invariant Measures -- 1. Ergodicity, Attractors and Bowen-Ruelle-Sinai Measures -- 2. Invariant Measures for Markov Maps -- 3. Constructing Invariant Measures by Inducing -- 4. Constructing Invariant Measures by Pulling Back -- 5. Transitive Maps Without Finite Continuous Measures -- 6. Frequency of Maps with Positive Liapounov Exponents in Families and Jakobson's Theorem -- 7. Some Further Remarks and Open Questions -- VI. Renormalization -- 1. The Renormalization Operator -- 2. The Real Bounds -- 3. Bounded Geometry -- 4. The PullBack Argument -- 5. The Complex Bounds -- 6. Riemann Surface Laminations -- 7. The Almost Geodesic Principle -- 8. Renormalization is Contracting -- 9. Universality of the Attracting Cantor Set -- 10. Some Further Remarks and Open Questions -- VII. Appendix -- 1. Some Terminology in Dynamical Systems -- 2. Some Background in Topology -- 3. Some Results from Analysis and Measure Theory -- 4. Some Results from Ergodic Theory -- 5. Some Background in Complex Analysis -- 6. Some Results from Functional Analysis. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
One-dimensional dynamics has developed in the last decades into a subject in its own right. Yet, many recent results are inaccessible and have never been brought together. For this reason, we have tried to give a unified ac count of the subject and complete proofs of many results. To show what results one might expect, the first chapter deals with the theory of circle diffeomorphisms. The remainder of the book is an attempt to develop the analogous theory in the non-invertible case, despite the intrinsic additional difficulties. In this way, we have tried to show that there is a unified theory in one-dimensional dynamics. By reading one or more of the chapters, the reader can quickly reach the frontier of research. Let us quickly summarize the book. The first chapter deals with circle diffeomorphisms and contains a complete proof of the theorem on the smooth linearizability of circle diffeomorphisms due to M. Herman, J.-C. Yoccoz and others. Chapter II treats the kneading theory of Milnor and Thurstonj also included are an exposition on Hofbauer's tower construction and a result on fuB multimodal families (this last result solves a question posed by J. Milnor). |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Functions of real variables. |
| 9 (RLIN) |
21103 |
|
|---|
| Topical term or geographic name entry element |
Probabilities. |
| 9 (RLIN) |
21104 |
|
|---|
| Topical term or geographic name entry element |
Real Functions. |
| 9 (RLIN) |
21105 |
|
|---|
| Topical term or geographic name entry element |
Probability Theory. |
| 9 (RLIN) |
21106 |
| 700 ## - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Strien, Sebastian van. |
| Relator term |
author. |
| Relationship |
aut |
| -- |
http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) |
21107 |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="https://doi.org/10.1007/978-3-642-78043-1">https://doi.org/10.1007/978-3-642-78043-1</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Koha item type |
e-Book |
