D. Treschev

activity

20032026

most citedHill's formula

23 citations · 53 across the 19 of their papers we have counts for

collaborators

21 papers

math.DS2026

Isonormal potentials in one degree of freedom

Dmitry Treschev

We consider the Hamiltonian system with one degree of freedom $x ˙ = y, y ˙ = - \partial V (x) / \partial x, x, y \in R$ with the smooth potential $V:{\ma…

math.DS2026

Integrable perturbations of polynomial Hamiltonian systems

Dmitry Treschev

We consider a Hamiltonian system on the symplectic space $(R^{2 n}, d y \land d x)$ with a real-analytic Hamiltonian $H : R^{2 n} \to R$ . We assume that…

math.DS2026

Combinatorics of Hamiltonian Normal Forms

Dmitry Treschev

We discuss algebraic and combinatorial aspects of the Hamiltonian normal form theory. The main objective is to describe the normal form near a singular point by an explicit formula…

math.DS2025

Another billiard problem

Sergey Bolotin, Dmitry Treschev

Let $(M, g)$ be a Riemannian manifold, $Ω \subset M$ a domain with boundary $Γ$ , and $ϕ$ a smooth function such that $ϕ ∣_{Ω} > 0$ , $\ph|_Γ= 0$, and $\nabla ϕ ∣_{Γ} \neq = 0$ . We study the geode…

math.AP2025

On the problem of stability of viscous shocks

Sergey Bolotin, Dmitry Treschev

We consider the problem of spectral stability of traveling wave solutions $u = γ (x - W t)$ for a system of viscous conservation laws $\partial_{t} u + \partial_{x} F (u) = \partial_{x}^{2} u$ . S…

math.DS2024

Normalization flow in the presence of a resonance

Dmitry Treschev

Following arXiv:2303.02992, we develop an approach to the Hamiltonian theory of normal forms based on continuous averaging. We concentrate on the case of normal forms near an ellip…