Equilibrium States for Piecewise Weakly Convex Interval Maps
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We prove the existence of equilibrium states for geometric potentials in a class of piecewise weakly convex interval maps. This class includes systems with indifferent fixed points and non-Markov partitions. Under additional hypotheses we also obtain uniqueness.
💡 Research Summary
The paper investigates thermodynamic formalism for a broad class of interval maps called “a‑convex transformations.” These are piecewise monotone, orientation‑preserving maps (T:
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