dynamics meaning in music Diaaheldin Taha (Washington) - A Gap Theorem Steinhaus Conjecture for General Interval Exchange

Teichmuller Dynamics
21 March 2018

Full title: A Gap Theorem (Steinhaus Conjecture) for General Interval Exchange Transformations via Zippered Rectangles

Abstract: The Three Gap Theorem, also known as Steinhaus Conjecture, is a historic result asserting that for any α∈(0,1) and any integer N≥1, the fractional parts of the sequence 0,α,2α,⋯,(N−1)α partition the unit interval into N subintervals having at most three distinct lengths. We are presenting:

* a geometric interpretition in terms of sections to flows on surfaces that provides yet another proof of TGT

* a similar (and independent) approach by Alan Haynes, Jens Marklof, and Andreas Strombergsson to TGT that proves TGT and higher dimensional analogues (linear forms)

* a gap theorem for orbits of general interval exchanges maps with optimal bound

If there is time, we will touch on some applications of TGT that are of contemporary interest.

dynamics meaning in music Diaaheldin Taha (Washington) - A Gap Theorem Steinhaus Conjecture for General Interval Exchange
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