Title page for ETD etd-07112005-185010


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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