arXiv - MATH - Dynamical Systems最新文献_第6页

Multislicing and effective equidistribution for random walks on some homogeneous spaces 某些均质空间上随机漫步的多重切分和有效等分布

arXiv - MATH - Dynamical Systems Pub Date : 2024-09-05 DOI: arxiv-2409.03300

Timothée Bénard, Weikun He

{"title":"Multislicing and effective equidistribution for random walks on some homogeneous spaces","authors":"Timothée Bénard, Weikun He","doi":"arxiv-2409.03300","DOIUrl":"https://doi.org/arxiv-2409.03300","url":null,"abstract":"We consider a random walk on a homogeneous space $G/Lambda$ where $G$ is\u0000$mathrm{SO}(2,1)$ or $mathrm{SO}(3,1)$ and $Lambda$ is a lattice. The walk\u0000is driven by a probability measure $mu$ on $G$ whose support generates a\u0000Zariski-dense subgroup. We show that for every starting point $x in G/Lambda$\u0000which is not trapped in a finite $mu$-invariant set, the $n$-step distribution\u0000$mu^{*n}*delta_{x}$ of the walk equidistributes toward the Haar measure.\u0000Moreover, under arithmetic assumptions on the pair $(Lambda, mu)$, we show\u0000the convergence occurs at an exponential rate, tempered by the obstructions\u0000that $x$ may be high in a cusp or close to a finite orbit. Our approach is substantially different from that of Benoist-Quint, whose\u0000equidistribution statements only hold in Ces`aro average and are not\u0000quantitative, that of Bourgain-Furman-Lindenstrauss-Mozes concerning the torus\u0000case, and that of Lindenstrauss-Mohammadi-Wang and Yang about the analogous\u0000problem for unipotent flows. A key new feature of our proof is the use of a new\u0000phenomenon which we call multislicing. The latter is a generalization of the\u0000discretized projection theorems `a la Bourgain and we believe it presents\u0000independent interest.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Ruelle's inequality and Pesin's formula for Anosov geodesic flows in non-compact manifolds 非紧凑流形中阿诺索夫大地流的鲁埃尔不等式和佩辛公式

arXiv - MATH - Dynamical Systems Pub Date : 2024-09-05 DOI: arxiv-2409.03207

Alexander Cantoral, Sergio Romaña

引用次数: 0

How noise affects memory in linear recurrent networks 噪声如何影响线性递归网络的记忆

arXiv - MATH - Dynamical Systems Pub Date : 2024-09-05 DOI: arxiv-2409.03187

JingChuan Guan, Tomoyuki Kubota, Yasuo Kuniyoshi, Kohei Nakajima

引用次数: 0

Magic Billiards: the Case of Elliptical Boundaries 神奇的台球：椭圆边界案例

arXiv - MATH - Dynamical Systems Pub Date : 2024-09-05 DOI: arxiv-2409.03158

Vladimir Dragović, Milena Radnović

引用次数: 0

Prolongation of solutions and Lyapunov stability for Stieltjes dynamical systems Stieltjes 动力系统解的延长和 Lyapunov 稳定性

arXiv - MATH - Dynamical Systems Pub Date : 2024-09-05 DOI: arxiv-2409.03408

Lamiae Maia, Noha El Khattabi, Marlène Frigon

引用次数: 0

Continuation and bifurcations of periodic orbits and symbolic dynamics in the Swift-Hohenberg equation 斯威夫特-霍恩伯格方程中周期轨道的延续和分岔以及符号动力学

arXiv - MATH - Dynamical Systems Pub Date : 2024-09-04 DOI: arxiv-2409.03036

Jakub Czwórnóg, Daniel Wilczak

引用次数: 0

Les Canards de Turing 图灵鸭

arXiv - MATH - Dynamical Systems Pub Date : 2024-09-04 DOI: arxiv-2409.02400

Theodore Vo, Arjen Doelman, Tasso J. Kaper

{"title":"Les Canards de Turing","authors":"Theodore Vo, Arjen Doelman, Tasso J. Kaper","doi":"arxiv-2409.02400","DOIUrl":"https://doi.org/arxiv-2409.02400","url":null,"abstract":"In this article, we study a system of reaction-diffusion equations in which\u0000the diffusivities are widely separated. We report on the discovery of families\u0000of spatially periodic canard solutions that emerge from {em singular Turing\u0000bifurcations}. The emergence of these spatially periodic canards asymptotically\u0000close to the Turing bifurcations, which are reversible 1:1 resonant Hopf\u0000bifurcations in the spatial ODE system, is an analog in spatial dynamics of the\u0000emergence of limit cycle canards in the canard explosions that occur\u0000asymptotically close to Hopf bifurcations in time-dependent ODEs. In the full\u0000PDE system, we show that for most parameter values under study the Turing\u0000bifurcation is sub-critical, and we present the results of some direct\u0000numerical simulations showing that several of the different types of spatial\u0000canard patterns are attractors in the prototypical PDE. To support the numerical discoveries, we use geometric desingularization and\u0000geometric singular perturbation theory to demonstrate the existence of these\u0000families of spatially periodic canards. Crucially, in the singular limit, we\u0000study a novel class of {em reversible folded singularities}. In particular,\u0000there are two reversible folded saddle-node bifurcations of type II (RFSN-II),\u0000each occurring asymptotically close to a Turing bifurcation. We derive\u0000analytical formulas for these singularities and show that their canards play\u0000key roles in the observed families of spatially periodic canard solutions.\u0000Then, for an interval of values of the bifurcation parameter further below the\u0000Turing bifurcation and RFSN-II point, the spatial ODE also has spatially\u0000periodic canard patterns, however these are created by a reversible folded\u0000saddle (instead of the RFSN-II). It also turns out that there is an interesting\u0000scale invariance, so that some components of some spatial canards exhibit\u0000nearly self-similar dynamics.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142195909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Noise-induced order in high dimensions 高维度的噪声诱导秩序

arXiv - MATH - Dynamical Systems Pub Date : 2024-09-04 DOI: arxiv-2409.02498

Huayan Chen, Yuzuru Sato

引用次数: 0

State Space Kriging model for emulating complex nonlinear dynamical systems under stochastic excitation 模拟随机激励下复杂非线性动力系统的状态空间克里金模型

arXiv - MATH - Dynamical Systems Pub Date : 2024-09-04 DOI: arxiv-2409.02462

Kai Chenga, Iason Papaioannoua, MengZe Lyub, Daniel Straub

引用次数: 0

Energy Transport in Random Perturbations of Mechanical Systems 机械系统随机扰动中的能量传输

arXiv - MATH - Dynamical Systems Pub Date : 2024-09-04 DOI: arxiv-2409.03132

Anna Maria Cherubini, Marian Gidea

引用次数: 0