5 citations · 5 across the 7 of their papers we have counts for
7 papers
On inverse problem of dynamics
M. Rudnev, V. Ten
We study the question whether for a natural Hamiltonian system on a two-dimensional compact configuration manifold, a single trajectory of sufficiently high energy is almost surely…
Integrability versus topology of configuration manifolds and domains of possible motions
M. Rudnev, V. Ten
We establish a generic sufficient condition for a compact -dimensional manifold bearing an integrable geodesic flow to be the -torus. As a complementary result, we show that…
A model for separatrix splitting near multiple resonances
M. Rudnev, V. Ten
We propose a model for local dynamics of a perturbed convex real-analytic Liouville-integrable Hamiltonian system near a resonance of multiplicity . Physically, the m…
A new integrable 3+1 dimensional generalization of the Burgers equation
M. Rudnev, A. V. Yurov, V. A. Yurov
A new nonlinear 3+1 dimensional evolution equation admitting the Lax pair is presented. In the case of one spatial dimension, the equation reduces to the Burgers equation. A method…
Endpoint bounds for the non-isotropic Falconer distance problem associated with lattice-like sets
A. Iosevich, M. Rudnev
Let be contained in the unit ball. Let , the Euclidean distance set of . Falconer conjectured that the has positive…
On combinatorial compexity of convex sequences
A. Iosevich, M. Rudnev, V. Ten
We obtain a good upper bound on the number of solutions of a diophantine equation arising from a strictly convex sequences of real numbers.