Author | Block, Louis Stuart. author |
---|---|

Title | Dynamics in One Dimension [electronic resource] / by Louis Stuart Block, William Andrew Coppel |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1992 |

Connect to | http://dx.doi.org/10.1007/BFb0084762 |

Descript | VIII, 252 p. online resource |

SUMMARY

The behaviour under iteration of unimodal maps of an interval, such as the logistic map, has recently attracted considerable attention. It is not so widely known that a substantial theory has by now been built up for arbitrary continuous maps of an interval. The purpose of the book is to give a clear account of this subject, with complete proofs of many strong, general properties. In a number of cases these have previously been difficult of access. The analogous theory for maps of a circle is also surveyed. Although most of the results were unknown thirty years ago, the book will be intelligible to anyone who has mastered a first course in real analysis. Thus the book will be of use not only to students and researchers, but will also provide mathematicians generally with an understanding of how simple systems can exhibit chaotic behaviour

CONTENT

Periodic orbits -- Turbulence -- Unstable manifolds and homoclinic points -- Topological dynamics -- Topological dynamics (continued) -- Chaotic and non-chaotic maps -- Types of periodic orbits -- Topological Entropy -- Maps of the circle

Mathematics
Mathematical analysis
Analysis (Mathematics)
Topology
Mathematics
Analysis
Topology