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pro vyhledávání: '"Yves, Colin"'
Autor:
de Verdìère, Yves Colin
Publikováno v:
Quarterly journal of pure and applied mathematics, 2023, 19 (4), pp.1839--1853
In this survey paper, I describe some aspects of the dynamics and the spectral theory of sub-Riemannian3D contact manifolds. We use Toeplitz quantization of the characteristic coneas introduced by Louis Boutet de Monvel and Victor Guillemin. We also
Externí odkaz:
http://arxiv.org/abs/2409.12665
This paper is motivated by recent works on inverse problems for acoustic wave propagation in the interior of gas giant planets. In such planets, the speed of sound is isotropic and tends to zero at the surface. Geometrically, this corresponds to a Ri
Externí odkaz:
http://arxiv.org/abs/2406.19734
In geophysical environments, wave motions that are shaped by the action of gravity and global rotation bear the name of gravito-inertial waves. We present a geometrical description of gravito-inertial surface waves, which are low-frequency waves exis
Externí odkaz:
http://arxiv.org/abs/2402.12992
Pancake-like vortices are often generated by turbulence in geophysical flows. Here, we study the inertia-gravity oscillations that can exist within such geophysical vortices, due to the combined action of rotation and gravity. We consider a fluid enc
Externí odkaz:
http://arxiv.org/abs/2402.10749
Autor:
de Verdière, Yves Colin, Li, Zhenhao
Publikováno v:
Prob. Math. Phys. 5 (2024) 735-751
We study a model of internal waves in an effectively 2D aquarium under periodic forcing. In the case when the underlying classical dynamics has sufficiently irrational rotation number, we prove that the energy of the internal waves remains bounded. T
Externí odkaz:
http://arxiv.org/abs/2306.13834
Publikováno v:
J.Math.Anal.App. 534, 128040 (2024)
Eigenvalue spectrum of the Laplacian on a metric graph with arbitrary but fixed vertex conditions is investigated in the limit as the lengths of all edges decrease to zero at the same rate. It is proved that there are exactly four possible types of e
Externí odkaz:
http://arxiv.org/abs/2306.00631
We reprove the fact, due to Backus, that the Poincar{\'e} operator in ellipsoids admits a pure point spectrum with polynomial eigenfunctions.We then show that the eigenvalues of the Poincar{\'e} operator restricted to polynomial vector fields of fixe
Externí odkaz:
http://arxiv.org/abs/2305.01369
We study spectral properties of sub-Riemannian Laplacians, which are hypoelliptic operators. The main objective is to obtain quantum ergodicity results, what we have achieved in the 3D contact case. In the general case we study the small-time asympto
Externí odkaz:
http://arxiv.org/abs/2212.02920
Autor:
de Verdière, Yves Colin
Publikováno v:
Advances Nonlinear Studies, 2023, 23, pp.20220054
We give a new proof ofan extension of the Chazarain-Duistermaat-Guillemin wave traceformula to the case of 3D-contact manifolds.We use a normal form allowing to reduce to the case of the Heisenberg group.
Externí odkaz:
http://arxiv.org/abs/2205.08744
Autor:
de Verdìère, Yves Colin
The goal of this paper is to study periodic geodesics for sub-Riemannian metrics on a contact 3D-manifold.We develop two rather independent subjects:1) The existence of closed geodesics spiraling around periodic Reeb orbits for a generic metric.2) Th
Externí odkaz:
http://arxiv.org/abs/2202.13743