Morse Decompositions for Periodic General Dynamical Systems and Differential Inclusions

2012 ◽  
Vol 20 (4) ◽  
pp. 519-549 ◽  
Author(s):  
Yejuan Wang ◽  
Desheng Li
Keyword(s):  
Dynamical Systems ◽  
Differential Inclusions ◽  
Morse Decompositions

On the Dynamics of Nonautonomous General Dynamical Systems and Differential Inclusions

2007 ◽  
Vol 16 (5-6) ◽  
pp. 651-671 ◽  
Author(s):  
Desheng Li ◽  
Yejuan Wang ◽  
Suyun Wang
Keyword(s):  
Dynamical Systems ◽  
Differential Inclusions

scholarly journals ATTRACTOR–REPELLER PAIR, MORSE DECOMPOSITION AND LYAPUNOV FUNCTION FOR RANDOM DYNAMICAL SYSTEMS

2008 ◽  
Vol 08 (04) ◽  
pp. 625-641 ◽  
Author(s):  
ZHENXIN LIU ◽  
SHUGUAN JI ◽  
MENGLONG SU
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Function ◽  
Metric Space ◽  
Stability Theory ◽  
Lyapunov Functions ◽  
Random Dynamical Systems ◽  
Morse Decomposition ◽  
Compact Metric Space ◽  
Morse Decompositions ◽  
The Stability

In the stability theory of dynamical systems, Lyapunov functions play a fundamental role. In this paper, we study the attractor–repeller pair decomposition and Morse decomposition for compact metric space in the random setting. In contrast to [7,17], by introducing slightly stronger definitions of random attractor and repeller, we characterize attractor–repeller pair decompositions and Morse decompositions for random dynamical systems through the existence of Lyapunov functions. These characterizations, we think, deserve to be known widely.

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