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Exponentially Small Splitting of Invariant Manifolds of Parabolic Points
 
Inmaculada Baldomá University of Barcelona, Barcelona, Spain
Ernest Fontich University of Barcelona, Barcelona, Spain
Exponentially Small Splitting of Invariant Manifolds of Parabolic Points
eBook ISBN:  978-1-4704-0390-4
Product Code:  MEMO/167/792.E
List Price: $63.00
MAA Member Price: $56.70
AMS Member Price: $37.80
Exponentially Small Splitting of Invariant Manifolds of Parabolic Points
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Exponentially Small Splitting of Invariant Manifolds of Parabolic Points
Inmaculada Baldomá University of Barcelona, Barcelona, Spain
Ernest Fontich University of Barcelona, Barcelona, Spain
eBook ISBN:  978-1-4704-0390-4
Product Code:  MEMO/167/792.E
List Price: $63.00
MAA Member Price: $56.70
AMS Member Price: $37.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1672004; 83 pp
    MSC: Primary 37; Secondary 70; 34

    We consider families of one and a half degrees of freedom Hamiltonians with high frequency periodic dependence on time, which are perturbations of an autonomous system.

    We suppose that the origin is a parabolic fixed point with non-diagonalizable linear part and that the unperturbed system has a homoclinic connection associated to it. We provide a set of hypotheses under which the splitting is exponentially small and is given by the Poincaré-Melnikov function.

    Readership

    Graduate students and research mathematicians interested in dynamical systems and ergodic theory.

  • Table of Contents
     
     
    • Chapters
    • 1. Notation and main results
    • 2. Analytic properties of the homoclinic orbit of the unperturbed system
    • 3. Parameterization of local invariant manifolds
    • 4. Flow box coordinates
    • 5. The extension theorem
    • 6. Splitting of separatrices
  • 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: 1672004; 83 pp
MSC: Primary 37; Secondary 70; 34

We consider families of one and a half degrees of freedom Hamiltonians with high frequency periodic dependence on time, which are perturbations of an autonomous system.

We suppose that the origin is a parabolic fixed point with non-diagonalizable linear part and that the unperturbed system has a homoclinic connection associated to it. We provide a set of hypotheses under which the splitting is exponentially small and is given by the Poincaré-Melnikov function.

Readership

Graduate students and research mathematicians interested in dynamical systems and ergodic theory.

  • Chapters
  • 1. Notation and main results
  • 2. Analytic properties of the homoclinic orbit of the unperturbed system
  • 3. Parameterization of local invariant manifolds
  • 4. Flow box coordinates
  • 5. The extension theorem
  • 6. Splitting of separatrices
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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