Recurrent orbits of subgroups of local complex analytic diffeomorphisms

Abstract

We show recurrent phenomena for orbits of groups of local complex analytic diffeomorphisms that have a certain subgroup or image by a morphism of groups that is non-virtually solvable. In particular we prove that a non-virtually solvable subgroup of local biholomorphisms has always recurrent orbits, i.e. there exists an orbit contained in its set of limit points.

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References in corpus (2)

• Local dynamics of intersections: V. I. Arnold's theorem revisited
• Closed Orbits and Integrability for singularities of complex vector fields in dimension three

Cited by in corpus (2)

• The solvable length of groups of local diffeomorphisms
• Complex ODEs, singularity theory and dynamics