Degenerate homoclinic bifurcations in complex dimension 2 - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2023

Degenerate homoclinic bifurcations in complex dimension 2

Bifurcations homoclines dégénérées en dimension complexe 2

Résumé

Unfolding homoclinic tangencies is the main source of bifurcations in 2-dimensional (real or complex) dynamics. When studying this phenomenon, it is common to assume that tangencies are quadratic and unfold with positive speed. Adapting to the complex setting an argument of Takens, we show that any 1-parameter family of 2-dimensional holomorphic diffeomorphisms unfolding an arbitrary non-persistent homoclinic tangency contains such quadratic tangencies. Combining this with recent results of Avila-Lyubich-Zhang and former results in collaboration with Lyubich, this yields the abundance of robust homoclinic tangencies in the bifurcation locus for complex Hénon maps. We also study bifurcations induced by families with persistent tangencies, which provide another approach to the complex Newhouse phenomenon.
Fichier principal
Vignette du fichier
degenerate.pdf (468.06 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04130921 , version 1 (16-06-2023)

Licence

Identifiants

Citer

Romain Dujardin. Degenerate homoclinic bifurcations in complex dimension 2. 2023. ⟨hal-04130921⟩
17 Consultations
31 Téléchargements

Altmetric

Partager

More