马可夫理论的研究
Recherches autour de la theorie de Markoff
摘要：
正文涉及在数论中的Markoff方程的一般化，从连续分数产生。它给出了这种新方程的完全解决方法，以及它们在代数和代数几何中的解释。这种代数方法是完成与有关Fuchsian群的分析发展。与Teichmuller理论穿孔环面的链接是完全描述，给他们的分类与减少理论。引用了关于黎曼曲面、测地线及其哈密顿研究的更一般的考虑，以及它们在物理、1/f噪声和zeta函数中的应用。提出了一些重要的设想。由于群GL（2，Z）中的分解结果，给出了Markoff理论出现在不同几何背景下的原因。
英文摘要：
The text deals with generalizations of the Markoff equation in number theory, arising from continued fractions. It gives the method for the complete resolution of such new equations, and their interpretation in algebra and algebraic geometry. This algebraic approach is completed with an analytical development concerning fuchsian groups. The link with the Teichmuller theory for punctured toruses is completely described, giving their classification with a reduction theory. More general considerations about Riemann surfaces, geodesics and their hamiltonian study are quoted, together with applications in physics, 1/f noise and zeta function. Ideas about important conjectures are presented. Reasons why the Markoff theory appears in different geometrical contexts are given, thanks to decomposition results in the group GL(2,Z).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
