Number Theory and Dynamical Systems

M. M. Dodson, J. A. G. Vickers (Herausgeber)

Buch | Softcover

184 Seiten

1989
Cambridge University Press (Verlag)
978-0-521-36919-0 (ISBN)

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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.

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.

Erscheint lt. Verlag	9.11.1989
Reihe/Serie	London Mathematical Society Lecture Note Series
Zusatzinfo	Worked examples or Exercises
Verlagsort	Cambridge
Sprache	englisch
Maße	152 x 229 mm
Gewicht	230 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
ISBN-10	0-521-36919-3 / 0521369193
ISBN-13	978-0-521-36919-0 / 9780521369190
Zustand	Neuware