Bifurcation of Maps and Applications
Elsevier (Publisher)
Published on 1. January 1979
231 pages
978-0-08-087147-9 (ISBN)
Description
Bifurcation of Maps and Applications
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Gerard Iooss
Bifurcation of Maps and Applications
Book
04/1979
Elsevier
€47.88
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Content
- Front Cover
- Bifurcation of Maps and Applications
- Copyright Page
- Contents
- Introduction
- CHAPTER I. Stability or instability of a fixed point of a map in a Banach space
- CHAPTER II. Bifurcation of fixed points in R
- 1. Fixed points
- 2. Points of period 2
- 3. The Poincaré map - orbital stability
- CHAPTER III. Hopf bifurcation in R2
- 1. Standard Hopf-bifurcation
- 2. Non-standard Hopf-bifurcation
- 3. Rotation number of the diffeomorphism restricted to the invariant bifurcated closed curve and weak resonance
- 4. Hopf-bifurcation for fields in R2
- 5. Bifurcation into a 2-dimensional invariant torus for a non-autonomous differential equation
- 6. Bifurcation into a 2-dimensional invariant torus for an autonomous differential equation
- 7. Exercise
- 8. Domain of attractivity and uniqueness of the invariant circle
- CHAPTER IV. Subharmonic bifurcations of fixed points in R2-strong resonance
- 1. The general study
- 2. Subharmonic bifurcations for a non-autonomous differential equation
- 3. Subharmonic bifurcations for an autonomous differential equation
- 4. Relation with the paper of Arnold and comments
- CHAPTER V. Invariant manifolds and applications
- 1. The hyperbolic case
- 2. The central case
- 3. Application to bifurcation problems
- 4. Applications to differential equations
- CHAPTER VI. Bifurcation of an invariant circle into an invars 2-torus for a one parameter family of maps
- 1. Introduction. Definitions
- 2. Main theorem and comments
- 3. Center manifold theorem
- 4. Proof of the main theorem. Step 1: Reduction to the dimension 2
- 5. Proof of the main theorem. Step 2: Persistence of invariant circles for µ != 0
- 6. Proof of the main theorem. Step 3: Bifurcation
- 7. An example
- BIBLIOGRAPHY
