Geometric Lorenz flows with historic behavior

Abstract

We will show that, in the the geometric Lorenz flow, the set of initial states which give rise to orbits with historic behavior is residual in a trapping region.

This paper was accepted in August 2016 for publication in Discrete & Continuous Dynamical Systems - Series A (DCDS-A) - AIMS

References in corpus (2)

• Takens' last problem and existence of non-trivial wandering domains
• On Takens' Last Problem: tangencies and time averages near heteroclinic networks

Cited by in corpus (6)

• Historic behavior in non-hyperbolic homoclinic classes
• Emergence via non-existence of averages
• Abundance of wild historic behavior
• Complete set of invariants for a Bykov attractor
• Topological entropy and Hausdorff dimension of irregular sets for non-hyperbolic dynamical systems
• Irregular sets for piecewise monotonic maps