DIFFERENTIAL GEOMETRY 
APPLIED TO 					          DYNAMICAL SYSTEMS
Mathematica files

by Jean-Marc Ginoux

Department of Mechanical Engineering
University du Sud Toulon Var
B.P. 20132
83947 LA Garde cedex 
ginoux@univ-tln.fr
http://ginoux.univ-tln.fr

All notebooks (.nb) on this CD are based on the Windows version of  Mathematica 6.0.1. To open the notebooks corresponding to Examples, double click on the button box "MF01". This will open new cells with the references of the example number, chapter and page.

Part I  Dynamical Systems

Chapter 1  Introduction

There are no Mathematica Files in Chapter 1.

Chapter 2  Dynamical Systems

"MF01"Free Fall

"MF02"Predator-prey model

"MF03"Inverted pendulum

"MF04"Saddle Focus

"MF05"First Limit cycle

"MF06" Unforced Duffing oscillator

"MF07" Lorenz Butterfly

"MF08" Spherical Pendulum

"MF09" Hénon - Heiles Hamiltonian

Chapter 3  Invariant Sets

"MF10" Unstable Manifold

Chapter 4  Local Bifurcations

"MF11" Nonuniqueness of the Centre Manifold

Chapter 5  Slow-Fast Dynamical Systems

"MF12" Geometric Singular Perturbation Method 2D - Van der Pol System

"MF13" Geometric Singular Perturbation Method 3D - Chua's System

Chapter 6  Integrability

"MF14" Integrable System

"MF15" General Integral

"MF16" General Integralof Homogeneous Dynamical Systems

"MF17" Multiplier of Homogeneous Dynamical Systems

"MF18" First Integral of Affine and Projective models

"MF19" Kapteyn-Bautin system

Part II  Differential Geometry

Chapter 7  Differential Geometry

There are no Mathematica Files in Chapter 7.

Chapter 8  Dynamical Systems

"MF20" Unforced Duffing oscillator

"MF21" Lorenz Model

Chapter 9  Invariant Sets

"MF22" Local Invariance

"MF23" Volterra-Lotka predator- prey model 2D

"MF24" Volterra-Lotka predator- prey model 3D

"MF25" Nondecomposable quadrics  -  (PRT) model

Chapter 10  Local Bifurcations

"MF26" Centre Manifold Approximation 2D

"MF27" Centre Manifold Approximation 3D

"MF28" Centre Manifold depending upon a parameter 2D - Duffing Oscillator

"MF29" Centre Manifold depending upon a parameter 3D - Chen's system

Chapter 11  Slow-Fast Dynamical Systems

"MF30" Flow Curvature Method vs Geometric Singular Perturbation Method 2D - Van der Pol system

"MF31" Flow Curvature Method vs Geometric Singular Perturbation Method 3D - Chua's system

"MF32" Non-singularly perturbed systems: Lorenz Model

Chapter 12  Integrability

"MF33" Van der Pol system

"MF34" First integral of Volterra- Lotka system

"MF35" First integral of quadratic system

Chapter 13  Inverse Problem

"MF36" Inverse Problem 2D - Van der Pol system

"MF37" Inverse Problem 3D - Lorenz model

Part III  Applications

Chapter 14  Dynamical Systems

"MF38" FitzHugh- Nagumo model 2D

"MF39" Pikovskii- Rabinovich-Trakhtengerts model 3D

Chapter 15  Invariant Sets - Integrability

"MF40" Pikovskii-Rabinovich-Trakhtengerts (PRT)

"MF41" Rikitake model

"MF42" Chua's model

"MF43" Lorenz model

Chapter 16  Local Bifurcations

"MF44" Chua's model

"MF45" Lorenz model

Chapter 17  Slow-Fast Dynamical Systems

Piecewise linear models 2D & 3D

"MF46" Van der Pol piecewise linear model

"MF47" Chua's piecewise linear model

Singularly perturbed systems 2D & 3D

"MF48" FitzHugh-Nagumo model

"MF49" Chua's cubic model

Slow-fast dynamical 2D & 3D

"MF50" Brusselator model

"MF51" Pikovskii-Rabinovich-Trakhtengerts model

"MF52" Rikitake model

Piecewise linear models 4D & 5D

"MF53" Chua's piecewise linear model

"MF54" Chua's piecewise linear model

Singularly perturbed systems 4D & 5D

"MF55" Chua's cubic model

"MF56" Chua's cubic model

"MF57" Hompolar Dynamo Model

"MF58" Mofatt model

"MF59" Magnetoconvection model

Non-Autonomous Dynamical Systems

"MF60" Forced Van der Pol