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On Generalized Markoff Equations and Their Interpretation

  • Serge Perrine
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 550)

Abstract

This article gives a generalization of the Markoff theory for diophantine equations:
$$ m^2 + \varepsilon _2 m_1^2 + \varepsilon _2 m_2^2 = (a + 1)mm_1 m_2 + \varepsilon _2 \partial Km_1 m_2 - um $$
It is shown how these equations are linked to finite sequences of integers. The arborescent structure of their solutions is given. The link is given with the analysis of the Markoff spectrum, and with the representation of the free group F2 in M(2, Z), the algebra of 2 x 2 matrices with integers coefficients.

Keywords

Riemann Surface Diophantine Equation Mapping Class Group Fuchsian Group Faithful Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Serge Perrine
    • 1
  1. 1.MetzFrance

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