# An Introduction to Chaotic Dynamical Systems

@inproceedings{Devaney1986AnIT, title={An Introduction to Chaotic Dynamical Systems}, author={Robert L. Devaney}, year={1986} }

Part One: One-Dimensional Dynamics Examples of Dynamical Systems Preliminaries from Calculus Elementary Definitions Hyperbolicity An example: the quadratic family An Example: the Quadratic Family Symbolic Dynamics Topological Conjugacy Chaos Structural Stability Sarlovskiis Theorem The Schwarzian Derivative Bifurcation Theory Another View of Period Three Maps of the Circle Morse-Smale Diffeomorphisms Homoclinic Points and Bifurcations The Period-Doubling Route to Chaos The Kneeding Theory…

## 2,897 Citations

### Chapter 2 Preliminaries of Nonlinear Dynamics and Chaos

- Physics
- 2019

This chapter provides a brief review of some concepts and tools related to the subject of the monograph – chaos suppression, chaos synchronization, and chaotification. After a quick review of the…

### Resonances in skew and reducible quasi-periodic Hopf bifurcations

- Mathematics
- 2000

Two types of quasi-periodic Hopf bifurcations are known, in which a Whitney smooth family of quasi-periodic attractors loses its hyperbolicity. One is the reducible case, where the normal linear…

### Structure change of stable and unstable manifolds in two-dimensional maps: Period-doubling bifurcation

- Mathematics
- 1992

### Chaos and quasi-periodicity in diffeomorphisms of the solid torus

- Mathematics
- 2010

This paper focuses on the parametric abundance and the 'Cantorial'
persistence under perturbations of a recently discovered class of strange
attractors for diffeomorphisms, the so-called…

### CHAOTIC BEHAVIOR OF DYNAMICAL SYSTEMS OF HOMEOMORPHISM ON UNIT INTERVAL

- Mathematics
- 2009

In this article, we studied that no homeomorphism on unit interval into itself is chaotic in the sense of R.L. Devaney. We also studied the behavior of orbits of points in the dynamical system…

### Dynamical Systems and Hyperbolicity

- Mathematics
- 2012

In this chapter, a definition of the dynamical system is discussed and some important classes like continuous-time and discrete-time systems, conservative and dissipativc systems, autonomous and non-autonomous systems are introduced.

### Robust and Nonrobust Dynamical Systems: Classification of Attractor Types

- Mathematics
- 2014

We consider a class of autonomous continuous-time dynamical systems with phase space dimension N ≥ 3. Besides robust systems similar to Andronov–Pontryagin systems on the plane, there appears a class…

### Periodicity versus Chaos in One-Dimensional Dynamics

- MathematicsSIAM Rev.
- 2001

It is shown that maps with strong chaotic properties appear with positive frequency in parameter space in the population models of the Ricker and the Hassell families.

### One-dimensional chaos in a system with dry friction: analytical approach

- Mathematics, Physics
- 2013

We introduce a new analytical method, which allows to find chaotic regimes in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered.…