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 |
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 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 167; 2004; 83 ppMSC: 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.
ReadershipGraduate students and research mathematicians interested in dynamical systems and ergodic theory.
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Table of Contents
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Chapters
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1. Notation and main results
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2. Analytic properties of the homoclinic orbit of the unperturbed system
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3. Parameterization of local invariant manifolds
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4. Flow box coordinates
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5. The extension theorem
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6. Splitting of separatrices
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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