English
Ciência_Iscte
Publicações
Descrição Detalhada da Publicação
Título Revista
European Journal of Pure and Applied Mathematics
Ano (publicação definitiva)
2025
Língua
Inglês
País
Estados Unidos da América
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Abstract/Resumo
After the fundamental work of Livschitz in [1, 2], various research directions emerged,
among which the following stand out: (i) the study of cocycles with values in groups and semigroups
beyond R, as well as the investigation of corresponding regularity results; (ii) the analysis of how
a certain degree of regularity (Ck for k = 1, 2, . . . , ∞, ?) of the cocycle can confer corresponding
regularity to the solution of the cohomological equation; and (iii) the study of higher-dimensional
cohomology naturally associated with the action of groups such as Zk or Rk. The aim of this article
is to present, as self-contained as possible, a review of the natural generalizations of the notions
of cocycles and cochains, as well as their corresponding results, in the study of cohomological
equations.
Agradecimentos/Acknowledgements
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Palavras-chave
Cocycle,Cohomological equation,Coboundary,Cochain,Livschitz theorem,Lie group,Anosov flow,Anosov diffeomorphism
Classificação Fields of Science and Technology
- Matemáticas - Ciências Naturais
