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Number Theory and Dynamical Systems

AUD$72.95 inc GST

Part of London Mathematical Society Lecture Note Series

Helmut Riissmann, J. A. G. Vickers, S. J. Patterson, Caroline Series, S. G. Dani, S. Raghavan, R. Weissauer, K. J. Falconer, J. Harrison, Michel Mendes France, J. V. Armitage
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  • Date Published: January 1990
  • availability: Available
  • format: Paperback
  • isbn: 9780521369190

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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.

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    Product details

    • Date Published: January 1990
    • format: Paperback
    • isbn: 9780521369190
    • length: 184 pages
    • dimensions: 229 x 152 x 11 mm
    • weight: 0.28kg
    • availability: Available
  • Table of Contents

    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.

  • Editors

    M. M. Dodson

    J. A. G. Vickers

    Contributors

    Helmut Riissmann, J. A. G. Vickers, S. J. Patterson, Caroline Series, S. G. Dani, S. Raghavan, R. Weissauer, K. J. Falconer, J. Harrison, Michel Mendes France, J. V. Armitage

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