New developments in the ergodic theory of nonlinear dynamical systems

1994 ◽  
Vol 346 (1679) ◽  
pp. 145-157 ◽  
Keyword(s):  
Dynamical Systems ◽  
Ergodic Theory ◽  
Nonlinear Dynamical Systems ◽  
Statistical Properties ◽  
Strange Attractors ◽  
New Developments ◽  
Nonlinear Dynamical ◽  
Henon Maps ◽  
Open Questions ◽  
Hyperbolic Dynamical Systems

The purpose of this paper is to give a survey of recent results on non-uniformly hyperbolic dynamical systems. The emphasis is on the existence of strange attractors and Sinai-Ruelle-Bowen measures for Henon maps, but we also describe results about statistical properties of such dynamical systems and state some of the open questions in this area.

Universal Approximation of Multiple Nonlinear Operators by Neural Networks

2002 ◽  
Vol 14 (11) ◽  
pp. 2561-2566 ◽  
Author(s):  
Andrew D. Back ◽  
Tianping Chen
Keyword(s):  
Neural Networks ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Universal Approximation ◽  
Nonlinear Operators ◽  
Nonlinear Dynamical ◽  
Open Questions

Recently, there has been interest in the observed capabilities of some classes of neural networks with fixed weights to model multiple nonlinear dynamical systems. While this property has been observed in simulations, open questions exist as to how this property can arise. In this article, we propose a theory that provides a possible mechanism by which this multiple modeling phenomenon can occur.

Superior Cantor Sets and Superior Devil Staircases

2010 ◽  
Vol 1 (1) ◽  
pp. 78-84 ◽  
Author(s):  
Mamta Rani ◽  
Sanjeev Kumar Prasad
Keyword(s):  
Dynamical Systems ◽  
Real World ◽  
Nonlinear Dynamical Systems ◽  
Cantor Set ◽  
Cantor Sets ◽  
Strange Attractors ◽  
Nonlinear Dynamical ◽  
The Universe ◽  
Real World Problems

Mandelbrot, in 1975, coined the term fractal and included Cantor set as a classical example of fractals. The Cantor set has wide applications in real world problems from strange attractors of nonlinear dynamical systems to the distribution of galaxies in the universe (Schroder, 1990). In this article, we obtain superior Cantor sets and present them graphically by superior devil’s staircases. Further, based on their method of generation, we put them into two categories.

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