The Resource Iterated maps on the interval as dynamical systems, Pierre Collet, JeanPierre Eckmann
Iterated maps on the interval as dynamical systems, Pierre Collet, JeanPierre Eckmann
Resource Information
The item Iterated maps on the interval as dynamical systems, Pierre Collet, JeanPierre Eckmann represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Iterated maps on the interval as dynamical systems, Pierre Collet, JeanPierre Eckmann represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 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 onedimensional dynamical systems
 Language
 eng
 Extent
 1 online resource (xi, 247 pages)
 Contents

 Introduction
 Part I. Motivation and interpretation ; Oneparameter 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 oneparameter families of maps ; Oneparameter families of maps
 Abundance of aperiodic behavior
 Universal scaling
 Multidimensional maps
 Isbn
 9780817630263
 Label
 Iterated maps on the interval as dynamical systems
 Title
 Iterated maps on the interval as dynamical systems
 Statement of responsibility
 Pierre Collet, JeanPierre Eckmann
 Subject

 Differentiable dynamical systems
 Differentiable dynamical systems
 Differentiable dynamical systems
 Electronic books
 Electronic bookss
 Iterative methods (Mathematics)
 Iterative methods (Mathematics)
 Iterative methods (Mathematics)
 Iterative methods (Mathematics)
 MATHEMATICS  Numerical Analysis
 Mappings (Mathematics)
 Mappings (Mathematics)
 Mappings (Mathematics)
 Mappings (Mathematics)
 Differentiable dynamical systems
 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 onedimensional dynamical systems
 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, JeanPierre Eckmann
 Antecedent source
 unknown
 Bibliography note
 Includes list of mathematical symbols, bibliographical references (pages 239244), 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 ; Oneparameter 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 oneparameter families of maps ; Oneparameter 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
 9780817630263
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9780817649272
 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, JeanPierre Eckmann
 Antecedent source
 unknown
 Bibliography note
 Includes list of mathematical symbols, bibliographical references (pages 239244), 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 ; Oneparameter 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 oneparameter families of maps ; Oneparameter 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
 9780817630263
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9780817649272
 Other physical details
 illustrations.
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)458575469
Subject
 Differentiable dynamical systems
 Differentiable dynamical systems
 Differentiable dynamical systems
 Electronic books
 Electronic bookss
 Iterative methods (Mathematics)
 Iterative methods (Mathematics)
 Iterative methods (Mathematics)
 Iterative methods (Mathematics)
 MATHEMATICS  Numerical Analysis
 Mappings (Mathematics)
 Mappings (Mathematics)
 Mappings (Mathematics)
 Mappings (Mathematics)
 Differentiable dynamical systems
Genre
Member of
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Iteratedmapsontheintervalasdynamical/MTNYQ6p1u44/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Iteratedmapsontheintervalasdynamical/MTNYQ6p1u44/">Iterated maps on the interval as dynamical systems, Pierre Collet, JeanPierre Eckmann</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>