De Aller-Bedste Bøger - over 12 mio. danske og engelske bøger
Levering: 1 - 2 hverdage

Heights of Polynomials and Entropy in Algebraic Dynamics

Bag om Heights of Polynomials and Entropy in Algebraic Dynamics

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.

Vis mere
  • Sprog:
  • Engelsk
  • ISBN:
  • 9781852331252
  • Indbinding:
  • Hardback
  • Sideantal:
  • 228
  • Udgivet:
  • 12. februar 1999
  • Størrelse:
  • 160x17x241 mm.
  • Vægt:
  • 512 g.
  • 8-11 hverdage.
  • 20. november 2024
På lager

Normalpris

Abonnementspris

- Rabat på køb af fysiske bøger
- 1 valgfrit digitalt ugeblad
- 20 timers lytning og læsning
- Adgang til 70.000+ titler
- Ingen binding

Abonnementet koster 75 kr./md.
Ingen binding og kan opsiges når som helst.

Beskrivelse af Heights of Polynomials and Entropy in Algebraic Dynamics

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.

Brugerbedømmelser af Heights of Polynomials and Entropy in Algebraic Dynamics