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
Resource Information
The item Iterated maps on the interval as dynamical systems, Pierre Collet, Jean-Pierre 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, Jean-Pierre 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 one-dimensional dynamical systems
- Language
- eng
- Extent
- 1 online resource (xi, 247 pages)
- 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
- Isbn
- 9780817649272
- 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
- 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 one-dimensional 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, Jean-Pierre Eckmann
- 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
- 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
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
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Iterated-maps-on-the-interval-as-dynamical/F9cDHLHmxQA/" 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/Iterated-maps-on-the-interval-as-dynamical/F9cDHLHmxQA/">Iterated maps on the interval as dynamical systems, Pierre Collet, Jean-Pierre 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>
