5 citations · 10 across the 4 of their papers we have counts for
5 papers
Bachet's game with lottery moves
Dmitry Dagaev, Ilya Schurov
Bachet's game is a variant of the game of Nim. There are objects in one pile. Two players take turns to remove any positive number of objects not exceeding some fixed number $m…
Duck factory on the two-torus: multiple canard cycles without geometric constraints
Ilya Schurov, Nikita Solodovnikov
Slow-fast systems on the two-torus are studied. As it was shown before, canard cycles are generic in such systems, which is in drastic contrast with the planar case. It is known th…
On the adjacency quantization in the equation modelling the Josephson effect
Alexey Glutsyuk, Dmitry Filimonov, Victor Kleptsyn +1
We investigate two-parametric family of non-autonomous ordinary differential equations on the two-torus $$\dot x=\frac{dx}{dt}=ν\sin x + a + s \sin t, \ a,ν,s\in\rr; \ ν\neq0 \text…
Duck farming on the two-torus: multiple canard cycles in generic slow-fast systems
Ilya V. Schurov
Generic slow-fast systems with only one (time-scaling) parameter on the two-torus have attracting canard cycles for arbitrary small values of this parameter. This is in drastic con…
Ducks on the torus: existence and uniqueness
Ilya Schurov
We show that there exist generic slow-fast systems with only one (time-scaling) parameter on the two-torus, which have canard cycles for arbitrary small values of this parameter. T…