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Discrete Integrable Systems: QRT Maps and Elliptic Surfaces

Johannes J. Duistermaat
TLDR
The QRT Map as discussed by the authors is the pencil of biquadratic curves in the projective plane of the QRT surface and is used to measure the distance between two points.
Abstract: 
The QRT Map.- The Pencil of Biquadratic Curves in .- The QRT surface.- Cubic Curves in the Projective Plane.- The Action of the QRT Map on Homology.- Elliptic Surfaces.- Automorphisms of Elliptic Surfaces.- Elliptic Fibrations with a Real Structure.- Rational elliptic surfaces.- Symmetric QRT Maps.- Examples from the Literature.- Appendices.

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Finiteness theorems on elliptical billiards and a variant of the Dynamical Mordell-Lang Conjecture

Pietro Corvaja, +1 more
- 21 Mar 2021 - 
TL;DR: In this article, the authors give some theorems for certain patterns in elliptical billiards, related to periodic trajectories, and interpret the statements through a variant of the dynamical Mordell-Lang conjecture.
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Hans Duistermaat's contributions to Poisson geometry

Reyer Sjamaar
- 25 Oct 2011 - 
TL;DR: In 2010, Duistermaat was scheduled to lecture in the 2010 School on Poisson Geometry at IMPA, but passed away suddenly as mentioned in this paper, and this is a record of a talk I gave at the 2010 Conference on Poison Geometry (the week after the School) to share some of my memories of him.