Number Theory and Dynamical Systems (eBook, PDF)

Redaktion: Dodson, M. M.

• Format: PDF

Produktbeschreibung

This volume contains selected contributions from a very successful meeting on Number Theory and Dynamical Systems held at the University of York in 1987. There are close and surprising connections between number theory and dynamical systems. One emerged last century from the study of the stability of the solar system where problems of small divisors associated with the near resonance of planetary frequencies arose. Previously the question of the stability of the solar system was answered in more general terms by the celebrated KAM theorem, in which the relationship between near resonance (and so Diophantine approximation) and stability is of central importance. Other examples of the connections involve the work of Szemeredi and Furstenberg, and Sprindzuk. As well as containing results on the relationship between number theory and dynamical systems, the book also includes some more speculative and exploratory work which should stimulate interest in different approaches to old problems.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 9. November 1989
• Englisch
• ISBN-13: 9780511892424
• Artikelnr.: 38204253

Inhaltsangabe

1. Non-degeneracy in the perturbation theory of integrable dynamical
systems Helmut Riissmann; 2. Infinite dimensional inverse function theorems
and small divisors J. A. G. Vickers; 3. Metric Diophantine approximation of
quadratic forms S. J. Patterson; 4. Symbolic dynamics and Diophantine
equations Caroline Series; 5. On badly approximable numbers, Schmidt games
and bounded orbits of flows S. G. Dani; 6. Estimates for Fourier
coefficients of cusp forms S. Raghavan and R. Weissauer; 7. The integral
geometry of fractals K. J. Falconer; 8. Geometry of algebraic continued
fractals J. Harrison; 9. Chaos implies confusion Michel Mendes France; 10.
The Riemann hypothesis and the Hamiltonian of a quantum mechanical system
J. V. Armitage.