Heights of Polynomials and Entropy in Algebraic Dynamics

Thomas Ward

ISBN 10: 1849968543 / ISBN 13: 9781849968546

Verlag: Springer London, 2010

Beschreibung

Druck auf Anfrage Neuware - Printed after ordering - 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.

Bestandsnummer des Verkäufers 9781849968546

Bibliografische Details

• Titel: Heights of Polynomials and Entropy in Algebraic Dynamics
• Verlag: Springer London
• Erscheinungsjahr: 2010
• Sprache: Englisch
• ISBN-10: 1849968543
• ISBN-13: 9781849968546
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 279B x 210 H x 13 T Millimeter Breite: 279 mm, Höhe: 210 mm, Tiefe: 13 mm
• Gewicht: 567 Gramm

Über diesen Titel

Inhaltsangabe

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.