Research Catalog

Combinatorial dynamics and entropy in dimension one

Title
Combinatorial dynamics and entropy in dimension one / Lluís Alsedà and Jaume Llibre, Michał Misiurewicz.
Author
Alsedà, Ll.
Publication
Singapore ; River Edge, NJ : World Scientific, ©1993.

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Details

Additional Authors
  • Llibre, Jaume.
  • Misiurewicz, Michał, 1948-
Description
xiv, 329 pages : illustrations; 23 cm.
Series Statement
Advanced series in nonlinear dynamics ; v. 5
Uniform Title
Advanced series in nonlinear dynamics ; v. 5.
Subject
  • Combinatorial dynamics
  • Mappings (Mathematics)
  • Entropy
  • entropy
  • Entropie
  • Afbeeldingen (wiskunde)
  • Eendimensionale systemen
  • Dynamique topologique
  • Applications (Mathématiques)
Bibliography (note)
  • Includes bibliographical references (p. 291-319) and index.
Contents
1. Preliminaries -- 1.1. General notation -- 1.2. Graphs, loops and cycles -- 2. Interval maps -- 2.1. The Sharkovskii Theorem -- 2.2. Maps with the prescribed set of periods -- 2.3. Forcing relation -- 2.4. Patterns for interval maps -- 2.5. Antisymmetry of the forcing relation -- 2.6. P-monotone maps and oriented patterns -- 2.7. Consequences of Theorem 2.6.13 -- 2.8. Stability of patterns and periods -- 2.9. Primary patterns -- 2.10. Extensions -- 2.11. Characterization of primary oriented patterns -- 2.12. More about primary oriented patterns -- 3. Circle maps -- 3.1. Liftings and degree of circle maps -- 3.2. Lifted cycles -- 3.3. Cycles and lifted cycles -- 3.4. Periods for maps of degree different from -1,0 and 1 -- 3.5. Periods for maps of degree 0 -- 3.6. Periods for maps of degree -1 -- 3.7. Rotation numbers and twist lifted cycles -- 3.8. Estimate of a rotation interval -- 3.9. Periods for maps of degree 1 -- 3.10. Maps of degree 1 with the prescribed set of periods -- 3.11. Other results -- 3.12. Appendix: Lifted patterns -- 4. Entropy -- 4.1. Definitions -- 4.2. Entropy for interval maps -- 4.3. Horseshoes -- 4.4. Entropy of cycles -- 4.5. Continuity properties of the entropy -- 4.6. Semiconjugacy to a map of a constant slope -- 4.7. Entropy for circle maps -- 4.8. Proof of Theorem 4.7.3.
ISBN
  • 9810213441
  • 9789810213442
LCCN
96143159
OCLC
  • ocm28840438
  • 28840438
  • SCSB-9040592
Owning Institutions
Princeton University Library