Nonadditive families of potentials: physical equivalence and some regularity relations
arXiv:2210.05926 · doi:10.1016/j.jde.2024.11.023
Abstract
We show that additive and asymptotically additive families of continuous functions with respect to suspension flows are physically equivalent. In particular, the equivalence result holds for hyperbolic flows and some classes of expansive flows in general. Moreover, we show how this equivalence result can be used to extend the nonadditive thermodynamic formalism and multifractal analysis. In the second part of this work, we obtain a Livšic-like result for nonadditive families of potentials and also address the Hölder and Bowen regularity problem for the physical equivalence relations with respect to hyperbolic symbolic flows.
A new update containing some corrections (proofs of Theorem 16 and Proposition 23), new comments and remarks