Examples of Morse decompositions for semigroups actions

• Braga Barros, Carlos J. ^[1] ; Tozatti, Hélio V. M. ^[1] ; Souza, Josiney A. ^[1]
  1. [1] Universidade Estadual de Maringá

     Universidade Estadual de Maringá

     Brasil

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 30, Nº. 1, 2011, págs. 65-75
• Idioma: inglés
• DOI: 10.4067/S0716-09172011000100007
• Enlaces
  • Texto completo
• Resumen

  • 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. 

• Referencias bibliográficas
  • Citas [1] Braga Barros, C. J. and Souza J. A. : Attractors and chain recurrence for semigroup actions. J. of Dyn. Diff. Eq. 22, pp. 723-740...
  • [2] Braga Barros, C. J. and Souza, J. A. : Finest Morse decompositions for semigroup actions on Fiber Bundles. J. of Dyn. Diff. Eq. 22, pp....
  • [3] Braga Barros, C. J., Souza, J. A. and Reis, R. A. : Dynamic Morse decompositions for semigroup of homeomorphisms and control systems....
  • [4] Braga Barros, C. J. and San Martin, L. A. B. : Chain transitive sets for flows on flag bundles. Forum Math. 19, pp. 19-60, (2007).
  • [5] Conley, C. : Isolated invariant sets and the Morse index. CBMS Regional Conf. Ser. in Math. 38, American Mathematical Society, (1978).
  • [6] Conley, C. : The gradient structure of a flow: I. Ergodic Theory Dynam. Systems 8, pp. 11-26, (1988).
  • [7] Ellis, D. B., Ellis, R. and Nerurkar, M. : The topological dynamics of semigroup actions. Trans. Amer. Math. Soc. 353, pp. 1279-1320,...
  • [8] Hirsch, W. M., Smith H. L. and Zhao, X. : Chain transitivity, attractivity and strong repellers for semidynamical systems. J. of Dyn....
  • [9] Patrao, M. : Morse decomposition of semiflows on topological spaces. J. of Dyn. Diff. Eq. 19, pp. 181-198, (2007).
  • [10] Patrao, M. and San Martin, L. A. B. : Semiflows on topological spaces: chain transitivity and semigroups. J. of Dyn. Diff. Eq. 19, pp....
  • [11] Patrao, M. and San Martin, L. A. B. : Morse decomposition of semi- flows on fiber bundles. Discrete and Continuous Dynamical Systems...