98 citations · 318 across the 23 of their papers we have counts for
24 papers
On Zeeman's collapsibility conjecture for non-standard polyhedra
Ivan Dynnikov
We prove that if Zeeman's collapsibility conjecture holds for standard polyhedra, then it holds in general.
An algorithm for comparing Legendrian knots
Ivan Dynnikov, Maxim Prasolov
We construct an algorithm to decide whether two given Legendrian or transverse links are equivalent. In general, the complexity of the algorithm is too high for practical implement…
Geometry of quasiperiodic functions on the plane
I. A. Dynnikov, A. Ya. Maltsev, S. P. Novikov
The present article proposes a review of the most recent results obtained in the study of Novikov's problem on the description of the geometry of the level lines of quasi-periodic…
Features of the motion of ultracold atoms in quasiperiodic potentials
Ivan Dynnikov, Andrei Maltsev
We consider here quasiperiodic potentials on the plane, which can serve as a "transitional link" between ordered (periodic) and chaotic (random) potentials. As can be shown, in alm…
Dynamical systems around the Rauzy gasket and their ergodic properties
Ivan Dynnikov, Pascal Hubert, Alexandra Skripchenko
At the beggining of the 80's, H.Masur and W.Veech started the study of generic properties of interval exchange transformations proving that almost every such transformation is uniq…
Rectangular diagrams of surfaces: the basic moves
Ivan Dynnikov, Maxim Prasolov
In earlier papers we introduced a representation of isotopy classes of compact surfaces embedded in the three-sphere by so called rectangular diagrams. The formalism proved useful…