Complete set of invariants for a Bykov attractor

Abstract

In this paper we consider an attracting heteroclinic cycle made by a 1-dimensional and a 2-dimensional separatrices between two hyperbolic saddles having complex eigenvalues. The basin of the global attractor exhibits historic behaviour and, from the asymptotic properties of these non-converging time averages, we obtain a complete set of invariants under topological conjugacy in a neighborhood of the cycle. These invariants are determined by the quotient of the real parts of the eigenvalues of the equilibria, a linear combination of their imaginary components and also the transition maps between two cross sections on the separatrices.

23 pages, 4 figures

References in corpus (3)

• Takens' last problem and existence of non-trivial wandering domains
• Geometric Lorenz flows with historic behavior
• Dense heteroclinic tangencies near a Bykov cycle

Cited by in corpus (1)

• Moduli of 3-dimensional diffeomorphisms with saddle-foci