Thermodynamic Formalism for Contracting Lorenz Flows |
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Authors: | Maria José Pacifico and Mike Todd |
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Institution: | 1.Instituto de Matemática,Universidade Federal do Rio de Janeiro,Rio de Janeiro,Brazil;2.Centro de Matemática da Universidade do Porto,Porto,Portugal |
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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 ^( j)]t(x,y,z):=-tlogJ(x,y,z)cu\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. |
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