Electronic ISBN:  9781470403904 
Product Code:  MEMO/167/792.E 
List Price:  $63.00 
MAA Member Price:  $56.70 
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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 nondiagonalizable 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 PoincaréMelnikov function.ReadershipGraduate 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


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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 nondiagonalizable 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 PoincaréMelnikov 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