Heights of Polynomials and Entropy in Algebraic Dynamics

Thomas Ward

ISBN 10: 1852331259 / ISBN 13: 9781852331252

Edité par Springer London, Springer London Feb 1999, 1999

A propos de cet article

Neuware -Arithmetic geometry and algebraic dynamical systems are flourishing areas of mathematics. Both subjects have highly technical aspects, yet both of fer a rich supply of down-to-earth examples. Both have much to gain from each other in techniques and, more importantly, as a means for posing (and sometimes solving) outstanding problems. It is unlikely that new graduate students will have the time or the energy to master both. This book is in tended as a starting point for either topic, but is in content no more than an invitation. We hope to show that a rich common vein of ideas permeates both areas, and hope that further exploration of this commonality will result. Central to both topics is a notion of complexity. In arithmetic geome try 'height' measures arithmetical complexity of points on varieties, while in dynamical systems 'entropy' measures the orbit complexity of maps. The con nections between these two notions in explicit examples lie at the heart of the book. The fundamental objects which appear in both settings are polynomi als, so we are concerned principally with heights of polynomials. By working with polynomials rather than algebraic numbers we avoid local heights and p-adic valuations.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 228 pp. Englisch.

N° de réf. du vendeur 9781852331252

Détails bibliographiques

• Titre: Heights of Polynomials and Entropy in Algebraic Dynamics
• Éditeur: Springer London, Springer London Feb 1999
• Date de parution: 1999
• Langue: anglais
• ISBN à 10 chiffres: 1852331259
• ISBN à 13 chiffres: 9781852331252
• Reliure: Buch
• État de l'article: Neu
• Dimensions: 241 L x 160 H x 17 P (en millimètres) 241 millimètres de largeur par 160 millimètres de hauteur par 17 millimètres de profondeur
• Poids: 512 grammes

A propos de ce titre

Synopsis

Arithmetic geometry and algebraic dynamical systems are flourishing areas of mathematics. Both subjects have highly technical aspects, yet both of- fer a rich supply of down-to-earth examples. Both have much to gain from each other in techniques and, more importantly, as a means for posing (and sometimes solving) outstanding problems. It is unlikely that new graduate students will have the time or the energy to master both. This book is in- tended as a starting point for either topic, but is in content no more than an invitation. We hope to show that a rich common vein of ideas permeates both areas, and hope that further exploration of this commonality will result. Central to both topics is a notion of complexity. In arithmetic geome- try 'height' measures arithmetical complexity of points on varieties, while in dynamical systems 'entropy' measures the orbit complexity of maps. The con- nections between these two notions in explicit examples lie at the heart of the book. The fundamental objects which appear in both settings are polynomi- als, so we are concerned principally with heights of polynomials. By working with polynomials rather than algebraic numbers we avoid local heights and p-adic valuations.