On maximal solution to infinite dimensional perturbed Riccati differential equations arising in stochastic control

2003 ◽  
Author(s):  
J. Baczynski ◽  
M.D. Fragoso
Keyword(s):  
Differential Equations ◽  
Stochastic Control ◽  
Maximal Solution ◽  
Infinite Dimensional ◽  
Riccati Differential Equations

scholarly journals State space decomposition for non-autonomous dynamical systems

2011 ◽  
Vol 141 (5) ◽  
pp. 957-974 ◽  
Author(s):  
Xiaopeng Chen ◽  
Jinqiao Duan
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
State Space ◽  
Decomposition Theorem ◽  
Navier Stokes ◽  
Locally Compact ◽  
Infinite Dimensional ◽  
The Lorenz System ◽  
A Chain ◽  
Autonomous Dynamical Systems

The decomposition of state spaces into dynamically different components is helpful for understanding dynamics of complex systems. A Conley-type decomposition theorem is proved for non-autonomous dynamical systems defined on a non-compact but separable state space. Specifically, the state space can be decomposed into a chain-recurrent part and a gradient-like part. This result applies to both non-autonomous ordinary differential equations on a Euclidean space (which is only locally compact), and to non-autonomous partial differential equations on an infinite-dimensional function space (which is not even locally compact). This decomposition result is demonstrated by discussing a few concrete examples, such as the Lorenz system and the Navier–Stokes system, under time-dependent forcing.

scholarly journals CANONICAL FORM OF THE EVOLUTION OPERATOR OF A TIME-DEPENDENT HAMILTONIAN IN THE THREE LEVEL SYSTEM

2011 ◽  
Vol 08 (03) ◽  
pp. 647-655
Author(s):  
KAZUYUKI FUJII
Keyword(s):  
Differential Equations ◽  
Canonical Form ◽  
Evolution Operator ◽  
Time Dependent ◽  
Level System ◽  
Riccati Differential Equations

In this paper we study the evolution operator of a time-dependent Hamiltonian in the three level system. The evolution operator is based on SU(3) and its dimension is eight, so we obtain three complex Riccati differential equations interacting with one another (which have been obtained by Fujii and Oike) and two real phase equations. This is a canonical form of the evolution operator.

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