Approximations of the Lagrange and Markov spectra

Abstract: The Lagrange and Markov spectra are closed subsets of the positive real numbers defined in terms of diophantine approximations. Their topological structures are quite involved: they begin with an explicit discrete subset accumulating at $3$, they end with a half-infinite ray of the form $[4.52\cdots,\infty)$, and the portions between $3$ and $4.52\cdots$ contain complicated Cantor sets. In this talk, we describe polynomial time algorithms to approximate (in Hausdorff topology) these spectra.

dynamical systemsnumber theory

Audience: researchers in the topic

( paper | slides )

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One World Numeration seminar

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