# Classification des cycles homoclines forces par symetrie dans R^4

Abstract : In this thesis we classify the
robust homoclinic cycles of $\mathbb{R}^4$ in presence of
symmetry. We limit our self to the case of a group G finite and,
without loss of generality, included in the orthogonal group
$O(4)$. We show that an infinite family of cycles exists; we give
the generators, a presentation and a detailed analysis of its
symmetry groups. The topology of the cycles is also studied.\\
These cycles
can
appear by a bifurcation from a trivial equilibrium so we can obtain
some
vector fields displaying such homoclinic cycles in the simplest
cases.
The numerical integration of such vector fields using the software
$\mathbf{Dstool}$ is possible; we visualize the projection of these cycles on
some planes.
Mots-clés :
Document type :
Theses
Domain :

https://tel.archives-ouvertes.fr/tel-00001813
Contributor : Nicola Sottocornola <>
Submitted on : Saturday, October 12, 2002 - 4:54:21 PM
Last modification on : Monday, October 12, 2020 - 10:27:25 AM
Long-term archiving on: : Friday, April 2, 2010 - 8:00:54 PM

### Identifiers

• HAL Id : tel-00001813, version 1

### Citation

Nicola Sottocornola. Classification des cycles homoclines forces par symetrie dans R^4. Mathématiques [math]. Université Nice Sophia Antipolis, 2002. Français. ⟨tel-00001813⟩

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