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Discrete Dynamical Systems and Difference Equations with Mathematica

Discrete Dynamical Systems and Difference Equations with Mathematica by Mustafa R.S. Kulenovic
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DYNAMICS OF ONE-DIMENSIONAL DYNAMICAL SYSTEMS
Introduction
Linear Difference Equations with Constant Coefficients
Linear Difference Equations with Variable Coefficients
Stability
Stability in the Non-Hyperbolic Case
Bifurcations
Dynamica Session
Symbolic Dynamics for One-Dimensional Maps
Dissipative Maps and Global Attractivity
Parametrisation and Poincaré Functional Equation
Exercises
DYNAMICS OF TWO-DIMENSIONAL DYNAMICAL SYSTEMS
Introduction
Linear Theory
Equilibrium Solutions
The Riccati Equation
Linearized Stability Analysis
Dynamica Session
Period Doubling Bifurcation
Lyapunov Numbers
Box Dimension
Semicycle Analysis
Stable and Unstable Manifold
Dynamica Session on Henon's Equation
Invariants
Lyapunov Functions, Stability, and Invariants
Dynamica Session on Lyness' Map
Dissipative Maps and Systems
Dynamica Session on Rational Difference Equations
Area-preserving Maps and Systems
Biology Applications Projects
Applications in Economics
Exercises
SYSTEMS OF DIFFERENCE EQUATIONS, STABILITY, AND SEMICYCLES
Introduction
Linear Theory
Stability of Linear Systems
The Routh-Hurwitz and Schur-Cohn Criterion
Nonlinear Systems and Stability
Limit Sets and Invariant Manifolds
Dissipative Maps
Stability of Difference Equations
Semicycle Analysis
Dynamica Session on Semicycles
Exercises
INVARIANTS AND RELATED LYAPUNOV FUNCTIONS
Introduction
Invariants for Linear Equations and Systems
Invariants and Corresponding Lyapunov Functions for Nonlinear Systems
Invariants of Special Class of Difference Equations
Applications
Dynamica Session on Invariants
Dynamica Session on Lyapunov Functions
Invariance under Lie Group Transformations
Exercises
DYNAMICS OF THREE-DIMENSIONAL DYNAMICAL SYSTEMS
Introduction
Dynamica Session on Third Order Difference Equations
Dissipative Difference Equation of Third Order
Dynamica Session on Local Asymptotic Stability of Period-Two Solution
Dynamica Session on Todd's Difference Equation
Biology Applications Projects
Exercises
FRACTALS GENERATED BY ITERATED FUNCTIONS SYSTEMS
Introduction
Basic Definitions and Results
Iterated Function System
Basic Results on Iterated Functions Systems
Calculation of Box Dimension for IFS
Dynamica Session
Exercises
BIBLIOGRAPHY
INDEX
CRC Press; February 2002
363 pages; ISBN 9781420035353
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Title: Discrete Dynamical Systems and Difference Equations with Mathematica
Author: Mustafa R.S. Kulenovic; Orlando Merino
 
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