Dynamical Systems V
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"Dynamical Systems V" by V.I. Arnold, V.S. Afrajmovich, Yu.S. Il'yashenko, L.P. Shil'nikov is a mathematics book and learning resource focused on Dynamics. Best for teachers, students, and readers looking for stronger mathematical understanding.
Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, previously published as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.
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"Dynamical Systems V" by V.I. Arnold, V.S. Afrajmovich, Yu.S. Il'yashenko, L.P. Shil'nikov is a mathematics book and learning resource focused on Dynamics. Best for teachers, students, and readers looking for stronger mathematical understanding.
Topic: Dynamics
Author: V.I. Arnold, V.S. Afrajmovich, Yu.S. Il'yashenko, L.P. Shil'nikov
Who this is for:
- Teachers and classroom instructors
- Students building subject mastery
- Readers looking for practical learning support
Why this book matters: It stands out as a practical math resource that helps explain concepts, strengthen problem-solving, and support classroom or independent learning.
Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, previously published as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.
| Author | V.I. Arnold, V.S. Afrajmovich, Yu.S. Il'yashenko, L.P. Shil'nikov |
| Publisher | Springer |
| Published | 1994-06-06 |
| ISBN-13 | 9783540181736 |
| Binding | Hardcover |
| Language | English |
| Subjects | Mathematics |
| Topic | Dynamics |
| Series | Encyclopaedia of Mathematical Sciences |
Format: Hardcover
Language: English
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