Local Dimensions and Quantization Dimensions in Dynamical Systems

Stochastic Dynamical Systems in Infinite Dimensions

In this article, we summarize some results on the existence and qualitative behavior of stochastic dynamical systems in infinite dimensions. The three main examples covered are stochastic systems with finite memory (stochastic functional differential equations-sfde’s), semilinear stochastic evolution equations (see’s) and stochastic partial differential equations (spde’s). Due to limitations of...

Output functions and fractal dimensions in dynamical systems.

We present a novel method for the calculation of the fractal dimension of boundaries in dynamical systems, which is in many cases many orders of magnitude more efficient than the uncertainty method. We call it the output function evaluation (OFE) method. We show analytically that the OFE method is much more efficient than the uncertainty method for boundaries with D<0.5, where D is the dimensio...

Companding and random quantization in several dimensions

Dynamical Systems in One and Two Dimensions: A Geometrical Approach

This chapter is intended as an introduction or tutorial to nonlinear dynamical systems in one and two dimensions with an emphasis on keeping the mathematics as elementary as possible. By its nature such an approach does not have the mathematical rigor that can be found in most textbooks dealing with this topic. On the other hand it may allow readers with a less extensive background in math to d...

Massera’s theorem for monotone dynamical systems in three dimensions

In this paper we give a variant of the classical second Massera’s theorem for threedimensional periodic systems, that satisfy different types of monotonicity assumptions.  2002 Elsevier Science (USA). All rights reserved.