2010
DOI: 10.1142/s0218127410027246
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Recent Developments in Dynamical Systems: Three Perspectives

Abstract: The aim of this paper is to give an account of some problems considered in past years in the setting of Dynamical Systems, some new research directions and also state some open problems Keywords: Topological entropy, Li-Yorke chaos, Lyapunov exponent, continua, nonautonomous systems, difference equations, ordinary and partial differential equations, set-valued dynamical system, global attractor, non-autonomous and random pullback attractors.

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Cited by 88 publications
(55 citation statements)
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References 169 publications
(191 reference statements)
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“…We can find a comparison of the two first and the three methods in [13] and [32], respectively. One can also find a recent review on the three methods in [4]. In the present work we use the third approach and we show the existence of the trajectory attractor of weak solutions to (7) and give some partial results related to its structure.…”
mentioning
confidence: 90%
“…We can find a comparison of the two first and the three methods in [13] and [32], respectively. One can also find a recent review on the three methods in [4]. In the present work we use the third approach and we show the existence of the trajectory attractor of weak solutions to (7) and give some partial results related to its structure.…”
mentioning
confidence: 90%
“…Let g 1G ≥ 0, g 22G , h 1G , h 12G , and h 22G ≥ 0 be the greatest values on the sphere S of the functions g 1 …”
Section: Bounded Solutions Of Quadratic Dynamical Systemsmentioning
confidence: 99%
“…Miller (1965) and Sell (1967aSell ( , b, 1971 developed the notion of skew product flows and their associated cocycle property. These ideas are further described from a pedagogical point of view in the recent review article by Balibrea et al (2010). With descriptions of "time evolution" appropriate to nonautonomous differential equations at hand, the building blocks of a geometrical theory can be developed.…”
Section: Nonautonomous Dynamical Systemsmentioning
confidence: 99%