The Many Faces of Lorenz Knots

Marco Abate
Additional contact information
Marco Abate: University of Pisa, Department of Mathemathics

A chapter in Imagine Math, 2012, pp 169-174 from Springer

Abstract: Abstract One of the greatest pleasures in doing mathematics (and one of the surest signs of being onto something really relevant) is discovering that two apparently completely unrelated objects actually are one and the same thing. This is what Étienne Ghys, of the École Normale Superieure de Lyon, did a few years ago (see [1] for the technical details), showing that the class of Lorenz knots, pertaining to the theory of chaotic dynamical systems and ordinary differential equations, and the class of modular knots, pertaining to the theory of 2-dimensional lattices and to number theory, coincide. In this short note we shall try to explain what Lorenz and modular knots are, and to give a hint of why they are the same. See also [2] for a more detailed but still accessible presentation, containing the beautiful pictures and animations prepared by Jos Leys [3], a digital artist, to illustrate Ghys’ results.

Keywords: Periodic Orbit; Modular Group; Left Wing; Integer Coefficient; Complex Logarithm (search for similar items in EconPapers)
Date: 2012
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-88-470-2427-4_16

Ordering information: This item can be ordered from
http://www.springer.com/9788847024274

DOI: 10.1007/978-88-470-2427-4_16

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().