Chaos in Discrete Dynamical Systems: A Visual Introduction in 2 Dimensions
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1997
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Chaos Theory is a synonym for dynamical systems theory, a branch of mathematics. Dynamical systems come in three flavors: flows (continuous dynamical systems), cascades (discrete, reversible, dynamical systems), and semi-cascades (discrete, irreversible, dynamical systems). Flows and semi-cascades are the classical systems iuntroduced by Poincare a centry ago, and are the subject of the extensively illustrated book: "Dynamics: The Geometry of Behavior," Addison-Wesley 1992 authored by Ralph Abraham and Shaw. Semi- cascades, also know as iterated function systems, are a recent innovation, and have been well-studied only in one dimension (the simplest case) since about 1950. The two-dimensional case is the current frontier of research. And from the computer graphcis of the leading researcher come astonishing views of the new landscape, such as the Julia and Mandelbrot sets in the beautiful books by Heinz-Otto Peigen and his co-workers. Now, the new theory of critical curves developed by Mira and his students and Toulouse provide a unique opportunity to explain the basic concepts of the theory of chaos and bifurcations for discete dynamical systems in two-dimensions. The materials in the book and on the accompanying disc are not solely developed only with the researcher and professional in mind, but also with consideration for the student. The book is replete with some 100 computer graphics to illustrate the material, and the CD-ROM contains full-color animations that are tied directly into the subject matter of the book, itself. In addition, much of this material has also been class-tested by the authors. The cross-platform CD also contains a software program called ENDO, which enables users to create their own 2-D imagery with X-Windows. Maple scripts are provided which give the reader the option of working directly with the code from which the graphcs in the book were |
| Physical Description: | 1 Online-Ressource (XXV, 246 p) |
| ISBN: | 9781461219361 9781461273479 |
| DOI: | 10.1007/978-1-4612-1936-1 |
Staff View
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| isbn | 9781461219361 9781461273479 |
| language | English |
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| spelling | Abraham, Ralph 1936- Verfasser (DE-588)115444254 aut Chaos in Discrete Dynamical Systems A Visual Introduction in 2 Dimensions by Ralph H. Abraham, Laura Gardini, Christian Mira New York, NY Springer New York 1997 1 Online-Ressource (XXV, 246 p) txt rdacontent c rdamedia cr rdacarrier Chaos Theory is a synonym for dynamical systems theory, a branch of mathematics. Dynamical systems come in three flavors: flows (continuous dynamical systems), cascades (discrete, reversible, dynamical systems), and semi-cascades (discrete, irreversible, dynamical systems). Flows and semi-cascades are the classical systems iuntroduced by Poincare a centry ago, and are the subject of the extensively illustrated book: "Dynamics: The Geometry of Behavior," Addison-Wesley 1992 authored by Ralph Abraham and Shaw. Semi- cascades, also know as iterated function systems, are a recent innovation, and have been well-studied only in one dimension (the simplest case) since about 1950. The two-dimensional case is the current frontier of research. And from the computer graphcis of the leading researcher come astonishing views of the new landscape, such as the Julia and Mandelbrot sets in the beautiful books by Heinz-Otto Peigen and his co-workers. Now, the new theory of critical curves developed by Mira and his students and Toulouse provide a unique opportunity to explain the basic concepts of the theory of chaos and bifurcations for discete dynamical systems in two-dimensions. The materials in the book and on the accompanying disc are not solely developed only with the researcher and professional in mind, but also with consideration for the student. The book is replete with some 100 computer graphics to illustrate the material, and the CD-ROM contains full-color animations that are tied directly into the subject matter of the book, itself. In addition, much of this material has also been class-tested by the authors. The cross-platform CD also contains a software program called ENDO, which enables users to create their own 2-D imagery with X-Windows. Maple scripts are provided which give the reader the option of working directly with the code from which the graphcs in the book were Mathematics Global analysis (Mathematics) Analysis Theoretical, Mathematical and Computational Physics Mathematik Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Chaotisches System (DE-588)4316104-2 s Differenzierbares dynamisches System (DE-588)4137931-7 s 1\p DE-604 Gardini, Laura 1952- Sonstige (DE-588)115524134 oth Mira, Christian Sonstige oth https://doi.org/10.1007/978-1-4612-1936-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Abraham, Ralph 1936- Chaos in Discrete Dynamical Systems A Visual Introduction in 2 Dimensions Mathematics Global analysis (Mathematics) Analysis Theoretical, Mathematical and Computational Physics Mathematik Differenzierbares dynamisches System (DE-588)4137931-7 gnd Chaotisches System (DE-588)4316104-2 gnd |
| subject_GND | (DE-588)4137931-7 (DE-588)4316104-2 |
| title | Chaos in Discrete Dynamical Systems A Visual Introduction in 2 Dimensions |
| title_auth | Chaos in Discrete Dynamical Systems A Visual Introduction in 2 Dimensions |
| title_exact_search | Chaos in Discrete Dynamical Systems A Visual Introduction in 2 Dimensions |
| title_full | Chaos in Discrete Dynamical Systems A Visual Introduction in 2 Dimensions by Ralph H. Abraham, Laura Gardini, Christian Mira |
| title_fullStr | Chaos in Discrete Dynamical Systems A Visual Introduction in 2 Dimensions by Ralph H. Abraham, Laura Gardini, Christian Mira |
| title_full_unstemmed | Chaos in Discrete Dynamical Systems A Visual Introduction in 2 Dimensions by Ralph H. Abraham, Laura Gardini, Christian Mira |
| title_short | Chaos in Discrete Dynamical Systems |
| title_sort | chaos in discrete dynamical systems a visual introduction in 2 dimensions |
| title_sub | A Visual Introduction in 2 Dimensions |
| topic | Mathematics Global analysis (Mathematics) Analysis Theoretical, Mathematical and Computational Physics Mathematik Differenzierbares dynamisches System (DE-588)4137931-7 gnd Chaotisches System (DE-588)4316104-2 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Theoretical, Mathematical and Computational Physics Mathematik Differenzierbares dynamisches System Chaotisches System |
| url | https://doi.org/10.1007/978-1-4612-1936-1 |
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