## An Introduction to Dynamical Systems: Continuous and DiscreteThis book gives an introduction into the ideas of dynamical systems. Its main emphasis is on the types of behavior which nonlinear systems of differential equations can exhibit. It is divided into two parts which can be read in either order: the first part treats the aspects coming from systems of nonlinear ordinary differential equations, and the second part is comprised of those aspects dealing with iteration of a function. For professionals with a strong mathematics background. |

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### Contents

Geometric Approach to Differential Equations | 7 |

Linear Systems | 13 |

Solutions of Nonlinear Equations | 67 |

Copyright | |

16 other sections not shown

### Other editions - View all

An Introduction to Dynamical Systems: Continuous and Discrete Rex Clark Robinson Limited preview - 2012 |

### Common terms and phrases

Assume asymptotically stable attracting fixed point attracting set basin of attraction bifurcation box dimension calculate called Cantor set chaotic attractor co(xo conjugacy Consider the system constant contains converge coordinates curve defined Definition dense dependence on initial determine diagonal differential equations doubling map Draw the phase eigenvalues eigenvector equal Example expansion Figure finite function give given goes to infinity goes to zero homoclinic integer intersection interval invariant set iterates Lemma linear map linear system logistic map Lyapunov exponents Lyapunov function map F Markov partition matrix of partial measure minus infinity negative nonlinear nullclines origin parameter values partial derivatives period-2 periodic orbit periodic points phase portrait plot Poincare point xo population proof properties repelling Section sensitive dependence solution stable and unstable symbol sequence system of differential tent map Theorem trajectory transition graph trapping region unstable manifold variables w-limit set