6533b86cfe1ef96bd12c80d8

RESEARCH PRODUCT

Internal perturbations of homoclinic classes:non-domination, cycles, and self-replication

Ch. BonattiS. CrovisierL. J. DíazN. Gourmelon

subject

Nonlinear Sciences::Chaotic DynamicsMathematics::Dynamical Systems37C29 37D20 37D30[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS]FOS: Mathematics[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Dynamical Systems (math.DS)Mathematics - Dynamical Systems

description

Conditions are provided under which lack of domination of a homoclinic class yields robust heterodimensional cycles. Moreover, so-called viral homoclinic classes are studied. Viral classes have the property of generating copies of themselves producing wild dynamics (systems with infinitely many homoclinic classes with some persistence). Such wild dynamics also exhibits uncountably many aperiodic chain recurrence classes. A scenario (related with non-dominated dynamics) is presented where viral homoclinic classes occur. A key ingredient are adapted perturbations of a diffeomorphism along a periodic orbit. Such perturbations preserve certain homoclinic relations and prescribed dynamical properties of a homoclinic class.

yearjournalcountryeditionlanguage
2010-11-12
https://hal.archives-ouvertes.fr/hal-00538112