**Memoirs of the American Mathematical Society**

2004;
83 pp;
Softcover

MSC: Primary 37;
Secondary 70; 34

Print ISBN: 978-0-8218-3445-9

Product Code: MEMO/167/792

List Price: $63.00

AMS Member Price: $37.80

MAA Member Price: $56.70

**Electronic ISBN: 978-1-4704-0390-4
Product Code: MEMO/167/792.E**

List Price: $63.00

AMS Member Price: $37.80

MAA Member Price: $56.70

# Exponentially Small Splitting of Invariant Manifolds of Parabolic Points

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*Inmaculada Baldomá; Ernest Fontich*

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

# Table of Contents

## Exponentially Small Splitting of Invariant Manifolds of Parabolic Points

- Contents v6 free
- Introduction vii8 free
- 1. Notation and main results 112 free
- 2. Analytic properties of the homoclinic orbit of the unperturbed system 718
- 3. Parameterization of local invariant manifolds 1526
- 4. Flow box coordinates 3748
- 5. The Extension Theorem 6374
- 6. Splitting of separatrices 6576
- References 8293