Type of Document	Dissertation
Author	Cazacu, George
Author's Email Address	cazacu@math.lsu.edu
URN	etd-07112005-185010
Title	Stability in Dynamical Polysystems
Degree	Doctor of Philosophy (Ph.D.)
Department	Mathematics
Advisory Committee	Advisor Name Title Jimmie Lawson Committee Chair Daniel Cohen Committee Member George Cochran Committee Member Peter Wolenski Committee Member William Adkins Committee Member Roger McNeil Dean's Representative
Keywords	attractor closed relation lyapunov function stability dynamical polysystem
Date of Defense	2005-06-30
Availability	unrestricted
Abstract A dynamical polysystem consists of a family of continuous dynamical systems, all acting on a given metric space. The first chapter of the present thesis shows a generalization of control systems via dynamical polysystems and establishes the equivalence of the two notions under certain lipschitz condition on the function defining the dynamics. The remaining chapters are focused on a basic theory of dynamical polysystems. Some topological properties of limit sets are described in Chapter 2. Chapters 3 and 4 provide characterizations for various notions of strong stability. Chapter 5 makes use of the theory of closed relations to study Lyapunov functions. Prolongations and absolute stability make the object of the last chapter.
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