165 citations · 773 across the 62 of their papers we have counts for
70 papers
The Hodograph Transform Between Thermodynamics and Relativity
Leonid Polterovich
In the contact-geometric approach to general relativity, the sky of an event - namely, the set of all incoming light rays - forms a Legendrian submanifold of the spherical cotangen…
A translation of "The Geometry of the Group of Symplectic Diffeomorphisms"
Leonid Polterovich
This book offers an introduction to Hofer's metric on the group of Hamiltonian diffeomorphisms. It presents results on the diameter, geodesics, and the growth of one-parameter subg…
Billiards and Hofer's Geometry
Mark Berezovik, Konstantin Kliakhandler, Yaron Ostrover +1
We present a link between billiards in convex plane domains and Hofer's geometry, an area of symplectic topology. For smooth strictly convex billiard tables, we prove that the Hofe…
A dichotomy for the Hofer growth of area preserving maps on the sphere via symmetrization
Lev Buhovsky, Ben Feuerstein, Leonid Polterovich +1
We prove that autonomous Hamiltonian flows on the two-sphere exhibit the following dichotomy: the Hofer norm either grows linearly or is bounded in time by a universal constant C.…
Lagrangian knots and unknots -- an essay
Leonid Polterovich, Felix Schlenk, with an appendix by Georgios Dimitroglou Rizell
In this essay dedicated to Yakov Eliashberg we survey the current state of the field of Lagrangian (un)knots, reviewing some constructions and obstructions along with a number of u…
Persistent transcendental Bézout theorems
Lev Buhovsky, Iosif Polterovich, Leonid Polterovich +2
An example of Cornalba and Shiffman from 1972 disproves in dimension two or higher a classical prediction that the count of zeros of holomorphic self-mappings of the complex linear…