Global Dynamical Systems Involving Generalized -Projection Operators and Set-Valued Perturbation in Banach Spaces

A new class of generalized dynamical systems involving generalizedf-projection operators is introduced and studied in Banach spaces. By using the fixed-point theorem due to Nadler, the equilibrium points set of this class of generalized global dynamical systems is proved to be nonempty and closed under some suitable conditions. Moreover, the solutions set of the systems with set-valued perturbation is showed to be continuous with respect to the initial value.

THREE-DIMENSIONAL ROTATIONS AND DISCRETE-TIME DYNAMICAL SYSTEMS: DISCRETE SYMMETRIES IN CHAOS-ORDER TRANSITIONS

It is shown that rotations in three dimensions induce two-dimensional noninvertible discrete time dynamical systems from which well-known one-dimensional mappings follow, for example, the logistic equation. The noninvertible mappings can be interpreted in terms of the dynamics of a kicked spherical top and display new forms of dynamics. The most interesting behavior of the generalized dynamical systems considered is a transition from a nearly homogeneous chaos to various forms of discrete symmetries on a unit sphere.