Geodesic
Relation between Levinson center, chain recurrent set and center of Birkhoff for compact dissipative dynamical systems
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2015), pp. 42-60 
David Cheban. Relation between Levinson center, chain recurrent set and center of Birkhoff for compact dissipative dynamical systems. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2015), pp. 42-60. http://geodesic.mathdoc.fr/item/BASM_2015_2_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we prove the analogues of Birkhoff's theorem for one-sided dynamical systems (both with continuous and discrete times) with noncompact space having a compact global attractor. The relation between Levinson center, chain recurrent set and center of Birkhoff is established for compact dissipative dynamical systems.

[1] Bondarchuk V. S., Dobrynskii V. A., “Dynamical Systems with Hyperbolic Center”, Functional and Differential-Difference Equations, Institute of Mathematics, Academy of Sciences of Ukraine, 1974, 13–40 (in Russian) | MR

[2] Bronstein I. U., Nonautonomous Dynamical Systems, Ştiintsa, Chişinău, 1984 (in Russian)

[3] Bronstein I. U., Burdaev B. P., “Chain Recurrence and Extensions of Dynamical Systems”, Mat. Issled., 55, 1980, 3–11 (in Russian) | MR

[4] Cheban David N., Global Attractors of Nonautonomous Dissipative Dynamical Systemst, Interdisciplinary Mathematical Sciences, 1, World Scientific, River Edge, NJ, 2004, xxvi+502 pp. | MR

[5] Cholewa J. W., Hale J. K., “Some Counterexamples in Dissipative Systems”, Dynamics of Continuous, Discrete and Impulsive Systems, 7 (2000), 159–176 | MR | Zbl

[6] Conley C., Isolated Invariant Sets and the Morse Index, Region. Conf. Ser. Math., 38, Am. Math. Soc., Providence, RI, 1978 | DOI | MR | Zbl

[7] Conley C., “The gradient structure of a flows: I”, Ergodic Theory Dynamical Systems, 8 (1988), 11–26 | DOI | MR | Zbl

[8] Hale J. K., “Stability and Gradient Dynamical Systems”, Rev. Math. Complut., 17:10 (2004), 7–57 | MR | Zbl

[9] Hirsch M. W., Smith H. L., Zhao X.-Q., “Chain Transitivity, Attractivity, and Strong Repellors for Semidynamical Systems”, J. Dyn. Diff. Eqns., 13:1 (2001), 107–131 | DOI | MR | Zbl

[10] Mike Hurley, “Chain recurrence, semiflows, and gradients”, Journal of Dynamics and Differential Equations, 7:3 (1995), 437–456 | DOI | MR | Zbl

[11] Patrao M., “Morse Decomposition of Semiflows on Topological Spaces”, Journal of Dinamics and Differential Equations, 19:1 (2007), 215–241 | MR

[12] Robinson C., Dynamical Systems: Stability, Symbolic Dynamics and Chaos, Studies in Advanced Mathematics, CRC Press, Boca Raton, Florida, 1995 | MR | Zbl

[13] Shcherbakov B. A., Stability by Poisson of Motions of Dynamical Systems and Solutions of Differential Equations, Ştiinţa, Chişinău, 1985 (in Russian)

[14] Introduction to Topological Dynamics, Noordhoff, Leyden, 1975 | MR | MR | Zbl