Thermodynamic formalism for contracting Lorenz flows

Details Thermodynamic formalism for contracting Lorenz flows Thermodynamic formalism for contracting Lorenz flows

2009-11-20

arxiv.org/abs/0911.4111v1

J. Stat. Phys. 139 (2010) 159-176

Mathematics

Dynamical Systems

Scientific paper

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 $\hat\phi_t(x,y, z):=-t\log J_{(x, y, z)}^{cu}$ 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.

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