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Abstract
This article studies past attractors and future repellers of topological cocycles conducted by a group G satisfying Ore's condition. The limit behaviour depends on the Green -pre-order on a right reversible semigroup S of G. An existence and uniqueness theorem for past attractors is proved. A topological method of extending functions is used in order to describe the past attractors by means of skew-product prolongations in the extended space. Illustrative examples of past attractor and future repeller are provided.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Funding
CNPq fellowship - Brazil (grant no 303011/2019-0).