Block, Louis Stuart.
Dynamics in One Dimension [electronic resource] / by Louis Stuart Block, William Andrew Coppel. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1992. - VIII, 252 p. online resource. - Lecture Notes in Mathematics, 1513 0075-8434 ; . - Lecture Notes in Mathematics, 1513 .
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.
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.
9783540470236
10.1007/BFb0084762 doi
Mathematics.
Global analysis (Mathematics).
Topology.
Mathematics.
Analysis.
Topology.
QA299.6-433
515
Dynamics in One Dimension [electronic resource] / by Louis Stuart Block, William Andrew Coppel. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1992. - VIII, 252 p. online resource. - Lecture Notes in Mathematics, 1513 0075-8434 ; . - Lecture Notes in Mathematics, 1513 .
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.
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.
9783540470236
10.1007/BFb0084762 doi
Mathematics.
Global analysis (Mathematics).
Topology.
Mathematics.
Analysis.
Topology.
QA299.6-433
515