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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
Available Formats:
Electronic 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 Click above image for expanded view Exponentially Small Splitting of Invariant Manifolds of Parabolic Points Inmaculada Baldomá University of Barcelona, Barcelona, Spain Ernest Fontich University of Barcelona, Barcelona, Spain Available Formats:  Electronic 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.

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
• Requests

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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.

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 reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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