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On limit behavior of skew‐product transformation semigroups
Author(s) -
Souza Josiney A.
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200190
Subject(s) - mathematics , skew , semigroup , transformation (genetics) , product (mathematics) , pure mathematics , mixing (physics) , limit (mathematics) , topology (electrical circuits) , direct product , special classes of semigroups , mathematical analysis , combinatorics , computer science , geometry , telecommunications , biochemistry , chemistry , physics , quantum mechanics , gene
This paper introduces both the notions of topological transitivity and topological mixing in the general setting of semigroup actions on topological spaces. A discussion on limit behavior of skew‐product transformation semigroups is presented. The main purpose is to characterize the lifts and the projections of recurrent points, attractors and Morse decompositions for transformation semigroups associated to skew‐product transformation semigroups. The results play a role to the existence of the finest Morse decomposition for control systems and their control flows.