Dmitry V. Treschev

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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

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 purely in terms of the…

math.DS2025

Another billiard problem

Sergey Bolotin, Dmitry Treschev

Let $(M, g)$ be a Riemannian manifold, $I^c ◯ \subset M$ a domain with boundary $I^$ , and $I ¨ $ a smooth function such that $I ¨ ∣_{I^} c ◯ > 0$ , $\ph|_Î= 0$, and $\nabla I ¨ ∣_{I^} \neq = 0$ . We study t…

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…

math.DS2024

On quantum Floquet theorem

Dmitry Treschev

We consider the SchrÃ¶dinger equation $ih \partial_{t} I ¨ = H I ¨ $ , $I ¨ = I ¨ (\cdot, t) \in L^{2} (T)$ . The operator $H = - \partial_{x}^{2} + V (x, t)$ includes smooth potential $V$ , which is…