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pro vyhledávání: '"Rousseau, Jerome"'
Nonnegative measures that are solutions to a transport equation with continuous coefficients have been widely studied. Because of the low regularity of the associated vector field, there is no natural flow since nonuniqueness of integral curves is th
Externí odkaz:
http://arxiv.org/abs/2407.02259
The celebrated geometric control condition of Bardos, Lebeau, and Rauch is necessary and sufficient for wave observability [1,7] and exact controllability. It requires that any point in phase-space be transported by the generalized geodesic flow to t
Externí odkaz:
http://arxiv.org/abs/2407.02255
We introduce three representative topics in semi-classical analysis. Starting from the correspondence between classical and quantum mechanics, basic semi-classical analysis tools and results are presented. The three topics are investigated in the lig
Externí odkaz:
http://arxiv.org/abs/2407.01998
For the wave and the Schr\"odinger equations we show how observability can be deduced from the observability of solutions localized in frequency according to a dyadic scale.
Externí odkaz:
http://arxiv.org/abs/2306.00536
The celebrated Rauch-Taylor/Bardos-Lebeau-Rauch geometric control condition is central in the study of the observability of the wave equation linking this property to high-frequency propagation along geodesics that are therays of geometric optics. Th
Externí odkaz:
http://arxiv.org/abs/2306.01023
We study the minimal distance between two orbit segments of length n, in a random dynamical system with sufficiently good mixing properties. This problem has already been solved in non-random dynamical system, and on average in random dynamical syste
Externí odkaz:
http://arxiv.org/abs/2209.13240
Autor:
Rousseau, Jerome, Todd, Mike
Given a dynamical system, we prove that the shortest distance between two $n$-orbits scales like $n$ to a power even when the system has slow mixing properties, thus building and improving on results of Barros, Liao and the first author. We also exte
Externí odkaz:
http://arxiv.org/abs/2209.06594
We consider a damped plate equation on an open bounded subset of R^d, or a smooth manifold, with boundary, along with general boundary operators fulfilling the Lopatinskii-Sapiro condition. The damping term acts on a region without imposing a geometr
Externí odkaz:
http://arxiv.org/abs/2109.01521
Autor:
Rousseau, Jerome
In this note, we studied the asymptotic behaviour of the length of the longest common substring for run-length encoded sequences. When the original sequences are generated by an $\alpha$-mixing process with exponential decay (or $\psi$-mixing with po
Externí odkaz:
http://arxiv.org/abs/2003.05500
Publikováno v:
In Composite Structures 15 October 2023 322
