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2011•Proyecciones (Antofagasta)Open access

Examples of Morse decompositions for semigroups actions

Carlos J. Braga Barros, Hélio V. M. Tozatti, Josiney A. Souza

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Abstract

The concepts of Morse decompositions and dynamic Morse decompositions are equivalent for flows. In this paper we show that these concepts are not equivalent for Morse decompositions of semigroups of homeomorphisms on topological spaces.We give an example of a dynamic Morse decompositions on compactifications of topological spaces. Other examples of Morse decompositions are also provided.

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The concepts of Morse decompositions and dynamic Morse decompositions are equivalent for flows. In this paper we show that these concepts are not equivalent for Morse decompositions of semigroups of homeomorphisms on topological spaces.We give an example of a dynamic Morse decompositions on compactifications of topological spaces. Other examples of Morse decompositions are also provided.

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Available abstract

The concepts of Morse decompositions and dynamic Morse decompositions are equivalent for flows. In this paper we show that these concepts are not equivalent for Morse decompositions of semigroups of homeomorphisms on topological spaces.We give an example of a dynamic Morse decompositions on compactifications of topological spaces. Other examples of Morse decompositions are also provided.

Key concepts: Morse code, Discrete Morse theory, Mathematics, Morse theory, Circle-valued Morse theory, Pure mathematics, Morse potential, Topology (electrical circuits)

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