Measures of intermediate entropies for star vector fields

2018/08/27 by Li, Ming, Shi, Yi, Wang, Shirou +1 · 2 citations
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.08700

Abstract

We prove that all star vector fields, including Lorenz attractors and multisingular hyperbolic vector fields, admit the intermediate entropy property. To be precise, if X is a star vector field with h_top(X)>0, then for any h∈ [0,h_top(X)), there exists an ergodic invariant measure μ of X such that h_μ(X)=h. Moreover, we show that the topological entropy is lower semi-continuous for star vector fields.

Cited by

• The Lyapunov Exponents of Hyperbolic Measures for C¹ Star Vector Fields on Three-dimensional Manifolds
• Entropy Flexibility of Dynamical Systems

Related

• Ergodic measures of intermediate entropies for dynamical systems with the approximate product property
• Equilibrium states for the classical Lorenz attractor and sectional-hyperbolic attractors in higher dimensions
• Measures of Intermediate Entropies for Skew Product Diffeomorphisms
• Entropy and Ergodic Measures for Toral Automorphisms
• Dimensional preimage entropies