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Nonlocal Bifurcations
 
Yu. Ilyashenko Moscow State University, Moscow, Russia
Weigu Li Beijing University, Beijing, People’s Republic of China
Nonlocal Bifurcations
Hardcover ISBN:  978-0-8218-0497-1
Product Code:  SURV/66
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1293-7
Product Code:  SURV/66.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-0497-1
eBook: ISBN:  978-1-4704-1293-7
Product Code:  SURV/66.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Nonlocal Bifurcations
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Nonlocal Bifurcations
Yu. Ilyashenko Moscow State University, Moscow, Russia
Weigu Li Beijing University, Beijing, People’s Republic of China
Hardcover ISBN:  978-0-8218-0497-1
Product Code:  SURV/66
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1293-7
Product Code:  SURV/66.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-0497-1
eBook ISBN:  978-1-4704-1293-7
Product Code:  SURV/66.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 661999; 286 pp
    MSC: Primary 34; 58;

    This book studies nonlocal bifurcations that occur on the boundary of the domain of Morse-Smale systems in the space of all dynamical systems. These bifurcations provide a series of fascinating new scenarios for the transition from simple dynamical systems to complicated ones. The main effects are the generation of hyperbolic periodic orbits, nontrivial hyperbolic invariant sets and the elements of hyperbolic theory. All results are rigorously proved and explained in a uniform way. The foundations of normal forms and hyperbolic theories are presented from the very first stages. The proofs are preceded by heuristic descriptions of the ideas. The book contains new results, and many results have not previously appeared in monograph form.

    Readership

    Graduate students and research mathematicians working in ordinary differential equations; physicists, engineers, computer scientists and mathematical biologists.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Preliminaries
    • 3. Bifurcations in the plane
    • 4. Homoclinic orbits of nonhyperbolic singular points
    • 5. Homoclinic tori and Klein bottles of nonhyperbolic periodic orbits: Noncritical case
    • 6. Homoclinic torus of a nonhyperbolic periodic orbit: Semicritical case
    • 7. Bifurcations of homoclinic trajectories of hyperbolic saddles
    • 8. Elements of hyperbolic theory
    • 9. Normal forms for local families: Hyperbolic case
    • 10. Normal forms for unfoldings of saddlenodes
  • Additional Material
     
     
  • Reviews
     
     
    • This book is clearly the most complete collection in existence of results for nonlocal bifurcations, excluding homoclinic tangencies. It is clearly written and would serve as a very good introduction to this field. The bibliography is surprisingly extensive, which is important since articles in this field are scattered over very many journals.

      Mathematical Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 661999; 286 pp
MSC: Primary 34; 58;

This book studies nonlocal bifurcations that occur on the boundary of the domain of Morse-Smale systems in the space of all dynamical systems. These bifurcations provide a series of fascinating new scenarios for the transition from simple dynamical systems to complicated ones. The main effects are the generation of hyperbolic periodic orbits, nontrivial hyperbolic invariant sets and the elements of hyperbolic theory. All results are rigorously proved and explained in a uniform way. The foundations of normal forms and hyperbolic theories are presented from the very first stages. The proofs are preceded by heuristic descriptions of the ideas. The book contains new results, and many results have not previously appeared in monograph form.

Readership

Graduate students and research mathematicians working in ordinary differential equations; physicists, engineers, computer scientists and mathematical biologists.

  • Chapters
  • 1. Introduction
  • 2. Preliminaries
  • 3. Bifurcations in the plane
  • 4. Homoclinic orbits of nonhyperbolic singular points
  • 5. Homoclinic tori and Klein bottles of nonhyperbolic periodic orbits: Noncritical case
  • 6. Homoclinic torus of a nonhyperbolic periodic orbit: Semicritical case
  • 7. Bifurcations of homoclinic trajectories of hyperbolic saddles
  • 8. Elements of hyperbolic theory
  • 9. Normal forms for local families: Hyperbolic case
  • 10. Normal forms for unfoldings of saddlenodes
  • This book is clearly the most complete collection in existence of results for nonlocal bifurcations, excluding homoclinic tangencies. It is clearly written and would serve as a very good introduction to this field. The bibliography is surprisingly extensive, which is important since articles in this field are scattered over very many journals.

    Mathematical Reviews
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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