# Exponentially Small Splitting of Invariant Manifolds of Parabolic Points

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*Inmaculada Baldomá; Ernest Fontich*

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.

#### 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