Coverart for item
The Resource Iterated maps on the interval as dynamical systems, Pierre Collet, Jean-Pierre Eckmann

Iterated maps on the interval as dynamical systems, Pierre Collet, Jean-Pierre Eckmann

Label
Iterated maps on the interval as dynamical systems
Title
Iterated maps on the interval as dynamical systems
Statement of responsibility
Pierre Collet, Jean-Pierre Eckmann
Creator
Contributor
Subject
Language
eng
Summary
Iterations of continuous maps of an interval to itself serve as the simplest examples of models for dynamical systems. These models present an interesting mathematical structure going far beyond the simple equilibrium solutions one might expect. If, in addition, the dynamical system depends on an experimentally controllable parameter, there is a corresponding mathematical structure revealing a great deal about interrelations between the behavior for different parameter values. This work explains some of the early results of this theory to mathematicians and theoretical physicists, with the additional hope of stimulating experimentalists to look for more of these general phenomena of beautiful regularity, which oftentimes seem to appear near the much less understood chaotic systems. Although continuous maps of an interval to itself seem to have been first introduced to model biological systems, they can be found as models in most natural sciences as well as economics. "Iterated Maps on the Interval as Dynamical Systems" is a classic reference used widely by researchers and graduate students in mathematics and physics, opening up some new perspectives on the study of dynamical systems. This book is a thorough and readable introduction to some aspects of the theory of one-dimensional dynamical systems
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorDate
1948-
http://library.link/vocab/creatorName
Collet, Pierre
Dewey number
518/.26
Illustrations
illustrations
Index
index present
Language note
English
LC call number
  • QA297.8
  • QA614.8
LC item number
  • .C655 2009eb
  • .C64 2009eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Eckmann, Jean Pierre
Series statement
Modern Birkhäuser classics
http://library.link/vocab/subjectName
  • Iterative methods (Mathematics)
  • Differentiable dynamical systems
  • Mappings (Mathematics)
  • MATHEMATICS
  • Differentiable dynamical systems
  • Mappings (Mathematics)
  • Iterative methods (Mathematics)
  • Differentiable dynamical systems
  • Iterative methods (Mathematics)
  • Mappings (Mathematics)
Label
Iterated maps on the interval as dynamical systems, Pierre Collet, Jean-Pierre Eckmann
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes list of mathematical symbols, bibliographical references (pages 239-244), and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
mixed
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Introduction -- Part I. Motivation and interpretation ; One-parameter families of maps -- Typical behavior for one map -- Parameter dependence -- Systematics of the stable periods -- On the relative frequency of periodic and aperiodic behavior -- Scaling and related predictions -- Higher dimensional systems -- Part II. Properties of individual maps ; Unimodal maps and their itineraries -- The calculus of itineraries -- Itineraries and orbits -- Negative Schwarzian derivative -- Homtervals -- Topological conjugacy -- Sensitive dependence on initial conditions -- Ergodic properties -- Part III. Properties of one-parameter families of maps ; One-parameter families of maps -- Abundance of aperiodic behavior -- Universal scaling -- Multidimensional maps
Control code
458575469
Dimensions
unknown
Extent
1 online resource (xi, 247 pages)
File format
unknown
Form of item
online
Isbn
9780817649272
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-0-8176-4927-2
Other physical details
illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)458575469
Label
Iterated maps on the interval as dynamical systems, Pierre Collet, Jean-Pierre Eckmann
Publication
Antecedent source
unknown
Bibliography note
Includes list of mathematical symbols, bibliographical references (pages 239-244), and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
mixed
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Introduction -- Part I. Motivation and interpretation ; One-parameter families of maps -- Typical behavior for one map -- Parameter dependence -- Systematics of the stable periods -- On the relative frequency of periodic and aperiodic behavior -- Scaling and related predictions -- Higher dimensional systems -- Part II. Properties of individual maps ; Unimodal maps and their itineraries -- The calculus of itineraries -- Itineraries and orbits -- Negative Schwarzian derivative -- Homtervals -- Topological conjugacy -- Sensitive dependence on initial conditions -- Ergodic properties -- Part III. Properties of one-parameter families of maps ; One-parameter families of maps -- Abundance of aperiodic behavior -- Universal scaling -- Multidimensional maps
Control code
458575469
Dimensions
unknown
Extent
1 online resource (xi, 247 pages)
File format
unknown
Form of item
online
Isbn
9780817649272
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-0-8176-4927-2
Other physical details
illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)458575469

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