Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of P(k)
François BertelootIMT - Institut de Mathématiques de Toulouse UMR5219 (UPS IMT, F-31062 Toulouse Cedex 9,
INSA Toulouse, F-31077 Toulouse,
France UT1, F-31042 Toulouse,
France UT2, F-31058 Toulouse,
Téléphone : 05.61.55.67.90 - France)Fabrizio BianchiIMT - Institut de Mathématiques de Toulouse UMR5219 (UPS IMT, F-31062 Toulouse Cedex 9,
INSA Toulouse, F-31077 Toulouse,
France UT1, F-31042 Toulouse,
France UT2, F-31058 Toulouse,
Téléphone : 05.61.55.67.90 - France)Christophe DupontIRMAR - Institut de Recherche Mathématique de Rennes (Campus de Beaulieu, bâtiments 22 et 23,
263 avenue du Général Leclerc, CS 74205
35042 RENNES Cédex - France)
2014en
ABI
Аннотация
We introduce a notion of stability for equilibrium measures in holomorphic\nfamilies of endomorphisms of CP(k) and prove that it is equivalent to the\nstability of repelling cycles and equivalent to the existence of some\nmeasurable holomorphic motion of Julia sets which we call equilibrium\nlamination. We characterize the corresponding bifurcations by the strict\nsubharmonicity of the sum of Lyapunov exponents or the instability of critical\ndynamics and analyze how repelling cycles may bifurcate. Our methods deeply\nexploit the properties of Lyapunov exponents and are based on ergodic theory\nand on pluripotential theory.\n
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