Dynamical systems

• Types
  • linear / nonlinear
  • discrete / continuos
  • symbolic/ analytic
  • deterministic/stochastic
  • one dimensional / two dimensional , ...

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From discrete to continuos dynamical system:
"To convert a map to a differential system
x[n+1]-x[n]-->dx[t]/dt
y[n+1]-y[n]-->dy[t]/dt
everything then converts to
{x[t],y[t]} "
Roger Bagula wrote on sci.fractals on 25.02.2006


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• Links:
  • "Internet suplement for basic complex analysis" by Marsden and Hoffman
  • Nonlinear Dynamics and Chaos by Ian Richards, Husaam Maudarbocus & Bernd Krauskopf.
  • R.de la Llave: Itroduction to the Theory of Computational Dynamics
  • Complex Analysis Harold V. McIntosh
  • wikipedia
  • Milnor - dynamics in one complex variable
  • Introduction to the theory of dynamical systems, stability and bifurcations by Johan Byström, Lars-Erik Persson and Fredrik Strömberg
  • Introduça~o aos Sistemas Dinâmicos: um Enfoque Prático com Maxima. Jaime E. Villate, Porto, Portugal, 2005, ISBN 972-99396-0-8 The textbook for the course on Dynamical Systems at the University of Porto, Portugal is freely available in the Internet (currently only in Portuguese). Examples in Maxima
  • Becker, Doerfler. Dynamical systems and fractals in Pascal [CUP, 1990] (pdf,410 p.,7670K,en,DVD11)
  • University of Rochester Course Math - 215: Fractals and computer graphics. Spring 1998- by Professor Douglas C. Ravenel using Mathemathica
  • chaos on the web  by Michael Cross
  • Invitation to Dynamical Systems by Edward R. Scheinerman,
  • Dynamical System web
  • Introduction to Mathematical physics: Dynamical Systems and Chaos Spring 2005
  • Introduction to Dynamic Systems  by Keith Clayton
    
  • J. Milnor Dynamics in One Complex Variable: Introductory Lectures.
    
  • Java PHASER Project A Universal Simulator for Dynamical Systems
    
  • differential equations
  • Simulation Methods in Physics by Harvey Gould and Jan Tobochnik
  • Dynamical Systems Theory by Nicholas B. Tufillaro
  • Dynamical Systems by George D. Birkhoff Publication Date: 1927
  • Chaos Book by P. Cvitanovi'c and all. Geometrical theory of dynamical systems. Nils Berglund's
  • Dynamical Systems and Fractals Lecture Notes David J. Wright
  • Hasselblatt and Katok: Handbook of Dynamical Systems

• Chris Preston: What You Need to Know to Knead
• SYMBOLIC DYNAMICS IN CHAOTIC SYSTEMS by Kai T. Hansen
• Symbolic Dynamics by Warren Weckesser
• Continuous Iteration of Dynamical Maps by R. Aldrovandi, L. P. Freitas
• Algebraic Geometry of Discrete Dynamics. The case of one variable by V. Dolotin, A. Morozov
• Helwig Löffelmann :Visualizing Local Properties and Characteristic Structures of Dynamical Systems
• Visualization of Complex Dynamical Systems at TECHNISCHE UNIVERSITÄT WIEN
• symbolic dynamic by Oliver Knill,

• One-Dimensional Topological Dynamics Jaume Llibre
• Two-Dimensional Topological Dynamics Jaume Llibre

• Michael Blank Round-off induced instabilities and some unusual arithmetics
• M. Blank: Pathologies generated by round-off in dynamical systems

• Software for Dynamical Systems Theory

Feel free to e-mail me!

Author: Adam Majewski adammaj1-at-o2-dot-pl

http://republika.pl/fraktal/

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