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Heights of Polynomials and Entropy in Algebraica Dynamics. / Everest
Titre : Heights of Polynomials and Entropy in Algebraica Dynamics. Type de document : texte imprimé Auteurs : Everest, Auteur ; Thomas Ward, Auteur Editeur : Springer New York Berlin Année de publication : 1999 Importance : 211p Format : 24x15.5 cm ISBN/ISSN/EAN : 978-1-85233-125-2 Langues : Anglais (eng) Langues originales : Anglais (eng) Mots-clés : Heights of Polynomials
Entropy - Arithmetic geometry
Algebraica DynamicsIndex. décimale : 510 Résumé : 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. Heights of Polynomials and Entropy in Algebraica Dynamics. [texte imprimé] / Everest, Auteur ; Thomas Ward, Auteur . - [S.l.] : Springer New York Berlin, 1999 . - 211p ; 24x15.5 cm.
ISBN : 978-1-85233-125-2
Langues : Anglais (eng) Langues originales : Anglais (eng)
Mots-clés : Heights of Polynomials
Entropy - Arithmetic geometry
Algebraica DynamicsIndex. décimale : 510 Résumé : 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. Exemplaires (1)
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