Abstract |
In this talk I want to discuss results with Mike Todd on the existence
and uniqueness of equilibrium states for multimodal
maps f:I→I with polynomial growth rates of derivatives along
the critical orbits. This requires more involved methods than for the
Collet-Eckmann class where these derivatives grow exponential. The class
of potentials include -t log|f'|, t ≈ 1, for which we
prove the analyticity of the pressure function except for the phase
transition occurring at t=1 for non-Collett-Eckmann maps.
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