Thermodynamical Formalism Associated with Inducing Schemes for One-dimensional Maps

Details Thermodynamical Formalism Associated with Inducing Schemes for One-dimensional Maps Thermodynamical Formalism Associated with Inducing Schemes for One-dimensional Maps

2005-11-24

arxiv.org/abs/math/0511599v1

Mathematics

Dynamical Systems

12 pages, to appear in Moscow Mathematical Journal

Scientific paper

For a smooth map f of a compact interval I admitting an inducing scheme we
establish a thermodynamical formalism, i.e., describe a class of real-valued
potential functions $\phi$ on I which admit a unique equilibrium measure
$\mu_\phi$. Our results apply to unimodal maps corresponding to a positive
Lebesgue measure set of parameters in a one-parameter transverse family.

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