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Morse decomposition for random dynamical systems
Random dynamical system Morse decomposition random attractor
2011/10/18
It is well-known that Morse decomposition is very useful to study the inner structure of invariant sets for given dynamical systems. Recently, Morse decomposition is established for random dynamical s...
Morse decomposition and Lyapunov functions for dynamical systems
Differential equation and dynamical system Morse decomposition Lyapunov function
2011/10/18
In this paper, we review Morse decomposition and Lyapunov functions. Most of the results are due to Conley and are known. Attractor-repeller pairs and Morse decompositions are very useful to study the...
Embedding smooth and formal diffeomorphisms through the Jordan-Chevalley decomposition
local diffeomorphism normal form embedding flow
2011/9/14
Abstract: In [Xiang Zhang, The embedding flows of $C^{\infty}$ hyperbolic diffeomorphisms, J. Differential Equations 250 (2011), no. 5, 2283-2298] Zhang proved that any local smooth hyperbolic diffeom...
A boundary matching micro/macro decomposition for kinetic equations
boundary matching micro/macro decomposition kinetic equations
2011/1/21
We introduce a new micro/macro decomposition of collisional kinetic equations which naturally incorporates the exact space boundary conditions.