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arXiv · 0911.4111

Thermodynamic formalism for contracting Lorenz flows

Maria Jose Pacifico·Mike Todd
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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 $\hat\phi_t(x,y, z):=-t\log J_{(x, y, z)}^{cu}$ 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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Maria Jose Pacifico, Mike Todd. 2009-11-20. Thermodynamic formalism for contracting Lorenz flows. https://doi.org/10.1007/s10955-010-9939-2

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