A convex analysis approach to entropy functions, variational principles and equilibrium states

• Autor(a) principal: Maria Pires de Carvalho
• Data de Publicação: 2022
• Outros Autores: Paulo Varandas, Andrzej Bis, Miguel Ângelo de Sousa Mendes
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: https://hdl.handle.net/10216/140723
• topic: Matemática; Mathematics

Using methods from Convex Analysis, for each generalized pressure function we define an upper semi-continuous affine entropy-like map, establish an abstract variational principle for both countably and finitely additive probability measures and prove that equilibrium states always exist. We show that this conceptual approach imparts a new insight on dynamical systems without a measure with maximal entropy, may be used to detect second-order phase transitions, prompts the study of finitely additive ground states for non-uniformly hyperbolic transformations and grants the existence of finitely additive Lyapunov equilibrium states for singular value potentials generated by linear cocycles over continuous self-maps.