Thermodynamic formalism for contracting Lorenz flows

Abstract

We study the expansion properties of the contracting Lorenz flow introduced by Rovella via thermodynamic formalism. Specifically, we prove the existence of an equilibrium state for the natural potential ${\hat{\varphi }}_t(x,y,z):=-t\log J_{(x,y,z)}^{cu}$ for the contracting Lorenz flow and for $t$ in an interval containing $[0,1]$. We also analyse the Lyapunov spectrum of the flow in terms of the pressure.

References in corpus (3)

• Singular-hyperbolic attractors are chaotic
• Equilibrium states for potentials with $\supϕ- \infϕ< \htop(f)$
• Lorenz like flows: exponential decay of correlations for the Poincaré map, logarithm law, quantitative recurrence

Cited by in corpus (7)

• Robust exponential decay of correlations for singular-flows
• On the statistical stability of families of attracting sets and the contracting Lorenz attractor
• Decay of correlations, quantitative recurrence and logarithm law for contracting Lorenz attractors
• Statistical properties of Lorenz like flows, recent developments and perspectives
• Noise induced order for skew-products over a non-uniformly expanding base
• On the Structure of Lorenz Maps
• Quenched decay of correlations for random contracting Lorenz maps