We introduce a notion of stability for equilibrium measures in holomorphic families of endomorphisms of ℙ k and prove that it is equivalent to the stability of repelling cycles and equivalent to the existence of some measurable holomorphic motion of Julia sets which we call equilibrium lamination. We characterize the corresponding bifurcations by the strict subharmonicity of the sum of Lyapunov exponents or the instability of critical dynamics and analyze how repelling cycles may bifurcate. Our methods deeply exploit the properties of Lyapunov exponents and are based on ergodic and pluripotential theory.

Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of ℙ(k)

Bianchi F;
2018-01-01

Abstract

We introduce a notion of stability for equilibrium measures in holomorphic families of endomorphisms of ℙ k and prove that it is equivalent to the stability of repelling cycles and equivalent to the existence of some measurable holomorphic motion of Julia sets which we call equilibrium lamination. We characterize the corresponding bifurcations by the strict subharmonicity of the sum of Lyapunov exponents or the instability of critical dynamics and analyze how repelling cycles may bifurcate. Our methods deeply exploit the properties of Lyapunov exponents and are based on ergodic and pluripotential theory.
2018
François, Berteloot; Bianchi, F; Christophe, Dupont
File in questo prodotto:
File Dimensione Formato  
StabPkV3.pdf

non disponibili

Tipologia: Versione finale editoriale
Licenza: NON PUBBLICO - accesso privato/ristretto
Dimensione 719.35 kB
Formato Adobe PDF
719.35 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Dynamical stability_preprint.pdf

accesso aperto

Tipologia: Versione finale editoriale
Licenza: Creative commons
Dimensione 523.26 kB
Formato Adobe PDF
523.26 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1201635
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 17
  • ???jsp.display-item.citation.isi??? 14
social impact