We establish the existence of equilibrium states for geometric potentials in a family of piecewise weakly convex interval maps. This family includes systems with indifferent fixed points and non-Markov partitions. Under specific conditions, we also prove the uniqueness of equilibrium states.
Equilibrium states for potentials with $\supφ- \infφ< \htop(f)$
Equilibrium states for interval maps: the potential $-t\log |Df|$
Equilibrium states in dynamical systems via geometric measure theory
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