Effective Ergodic Theory: Parabolic and Hyperbolic

有效的遍历理论:抛物线和双曲线

基本信息

  • 批准号:
    2154208
  • 负责人:
  • 金额:
    $ 42.44万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2022
  • 资助国家:
    美国
  • 起止时间:
    2022-06-15 至 2027-05-31
  • 项目状态:
    未结题

项目摘要

The project is devoted to the study of long-term behavior of a class of dynamical systems, called parabolic, which display sub-exponential (polynomial) divergence of nearby orbits. In contrast with hyperbolic dynamical systems, which display exponential divergence of orbits, parabolic systems are much less understood. Hyperbolic systems will also be studied insofar they appear as auxiliary tools in the study of parabolic ones, which are the main focus. The research will emphasize quantitative aspects that are relevant for applications. The project aims to advance our fundamental knowledge of dynamical systems and to develop new ideas and new methods of mathematical investigation with potential applications to geometry and number theory and thus indirectly to other scientific subjects. Also, since parabolic behavior appears in Hamiltonian mechanics, the project can directly advance our understanding of simple mathematical models of classical physical systems (billiards in polygons, statistical mechanics, planetary motions). Research training and mentoring of students and postdocs is an important goal of the project, with particular attention to members of underrepresented groups.The investigator will carry out research in several directions (effective weak mixing of translation flows, Ruelle asymptotics, dynamics on character varieties) and will continue work on longstanding open questions such as on effective ergodicity for non-horospherical unipotent flows (effective Ratner theory), optimal bounds on Weyl sums for higher degree polynomials, the ergodic theory of geodesic flows on flat surfaces and of billiards in non-rational polygons, as well as the ergodic and spectral theory of smooth parabolic flows. An important approach to parabolic systems, often called renormalization approach, replaces the direct studies of the parabolic dynamics with that of an auxiliary hyperbolic system, which is easier to understand by methods of hyperbolic theory (invariant manifolds, Lyapunov exponents). Motivated by recent interest in the relation between parabolic and hyperbolic dynamics via renormalization, the investigator has broadened his research with work on exponential decay of correlations and Ruelle asymptotics for hyperbolic systems from the point of view of the effective (polynomial) equidistribution of unstable foliations, and will further pursue research on the interplay between effective equidistribution in parabolic dynamics and effective mixing in hyperbolic dynamics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
该项目致力于研究一类称为抛物线的动力系统的长期行为,该系统显示附近轨道的次指数(多项式)发散。与双曲型动力系统相比,抛物型动力系统的轨道呈指数发散,人们对抛物型动力系统的了解要少得多。 双曲系统也将被研究,因为它们在抛物系统的研究中作为辅助工具出现,这是主要的焦点。研究将强调与应用相关的定量方面。该项目旨在推进我们的动力系统的基础知识,并开发新的思想和数学研究的新方法,具有潜在的应用几何和数论,从而间接地对其他科学学科。此外,由于抛物行为出现在哈密顿力学中,该项目可以直接促进我们对经典物理系统(多边形台球,统计力学,行星运动)的简单数学模型的理解。 对学生和博士后的研究培训和指导是该项目的一个重要目标,特别关注代表性不足的群体。(平移流的有效弱混合,Ruelle渐近,并将继续致力于长期悬而未决的问题,如非horosphere单幂流的有效遍历性(有效的拉特纳理论),最佳界限外尔和高次多项式,遍历理论的测地线流平面和台球在非理性多边形,以及遍历和光谱理论的光滑抛物流。抛物系统的一个重要方法,通常称为重整化方法,用辅助双曲系统代替抛物动力学的直接研究,这更容易通过双曲理论的方法(不变流形,李雅普诺夫指数)来理解。 受最近通过重正化在抛物和双曲动力学之间的关系的兴趣的激励,研究者从有效的角度扩展了他的研究,研究了双曲系统的相关性的指数衰减和Ruelle渐近性。(多项式)不稳定叶理的等分布,并将进一步研究抛物动力学中的有效等分布与双曲动力学中的有效混合之间的相互作用。该奖项反映了NSF的法定使命,并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

项目成果

期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ monograph.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ sciAawards.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ conferencePapers.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ patent.updateTime }}

Giovanni Forni其他文献

MP72-17 ROBOT-ASSISTED PARTIAL NEPHRECTOMY FOR COMPLEX CASES (PADUA SCORE = 10): RESULTS FROM A MULTICENTER EXPERIENCE AT THREE HIGH-VOLUME CENTERS
  • DOI:
    10.1016/j.juro.2017.02.2253
  • 发表时间:
    2017-04-01
  • 期刊:
  • 影响因子:
  • 作者:
    Giovanni Lughezzani;Nicolo' Buffi;Giuliana Lista;Davide Maffei;Giovanni Forni;Nicola Fossati;Alessandro Larcher;Massimo Lazzeri;Alberto Saita;Paolo Casale;Giorgio Guazzoni;Jim Porter;Alex Mottrie
  • 通讯作者:
    Alex Mottrie
Characteristics, Outcomes, and Long-Term Survival of Patients With Heart Failure Undergoing Inpatient Cardiac Rehabilitation
  • DOI:
    10.1016/j.apmr.2021.10.014
  • 发表时间:
    2022-05-01
  • 期刊:
  • 影响因子:
  • 作者:
    Domenico Scrutinio;Pietro Guida;Andrea Passantino;Simonetta Scalvini;Maurizio Bussotti;Giovanni Forni;Raffaella Vaninetti;Maria Teresa La Rovere
  • 通讯作者:
    Maria Teresa La Rovere
PD19-01 ACTIVE SURVEILLANCE FOR NON-MUSCLE INVASIVE BLADDER CANCER (NMIBC): RESULT FROM BLADDER CANCER ITALIAN ACTIVE SURVEILLANCE (BIAS) PROJECT.
  • DOI:
    10.1016/j.juro.2017.02.874
  • 发表时间:
    2017-04-01
  • 期刊:
  • 影响因子:
  • 作者:
    Rodolfo Hurle;Massimo Lazzeri;Giovanni Lughezzani;NicolòMaria Buffi;Alberto Saita;Luisa Pasini;Silvia Zandegiacomo;Alessio Benetti;Giovanni Forni;Piergiuseppe Colombo;Roberto Peschechera;Paolo Casale;Giuliana Lista;Pasquale Cardone;Giorgio Guazzoni
  • 通讯作者:
    Giorgio Guazzoni
Homology and cohomology with compact supports forq-convex spaces
Incremental prognostic value of functional impairment assessed by 6-min walking test for the prediction of mortality in heart failure
通过 6 分钟步行测试评估功能障碍的增量预后价值,以预测心力衰竭的死亡率
  • DOI:
  • 发表时间:
    2024
  • 期刊:
  • 影响因子:
    4.6
  • 作者:
    D. Scrutinio;Pietro Guida;M. L. La Rovere;Laura Adelaide Dalla Vecchia;Giovanni Forni;R. Raimondo;S. Scalvini;A. Passantino
  • 通讯作者:
    A. Passantino

Giovanni Forni的其他文献

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

{{ truncateString('Giovanni Forni', 18)}}的其他基金

Beyond Renormalization in Parabolic Dynamics
抛物线动力学中的重正化之外
  • 批准号:
    1600687
  • 财政年份:
    2016
  • 资助金额:
    $ 42.44万
  • 项目类别:
    Continuing Grant
Ergodic Theory of Parabolic Flows
抛物线流的遍历理论
  • 批准号:
    1201534
  • 财政年份:
    2012
  • 资助金额:
    $ 42.44万
  • 项目类别:
    Continuing Grant
Parabolic Dynamics
抛物线动力学
  • 批准号:
    0800673
  • 财政年份:
    2008
  • 资助金额:
    $ 42.44万
  • 项目类别:
    Continuing Grant
FRG: Rational billiards and geometry and dynamics on Teichmuller Space
FRG:Teichmuller 空间上的理性台球以及几何和动力学
  • 批准号:
    0244463
  • 财政年份:
    2003
  • 资助金额:
    $ 42.44万
  • 项目类别:
    Standard Grant

相似海外基金

Ergodic theory and multifractal analysis for non-uniformly hyperbolic dynamical systems with a non-compact state space
非紧状态空间非均匀双曲动力系统的遍历理论和多重分形分析
  • 批准号:
    24K06777
  • 财政年份:
    2024
  • 资助金额:
    $ 42.44万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Interplay between Ergodic Theory, Additive Combinatorics and Ramsey Theory
遍历理论、加法组合学和拉姆齐理论之间的相互作用
  • 批准号:
    DP240100472
  • 财政年份:
    2024
  • 资助金额:
    $ 42.44万
  • 项目类别:
    Discovery Projects
CAREER: Harmonic Analysis, Ergodic Theory and Convex Geometry
职业:调和分析、遍历理论和凸几何
  • 批准号:
    2236493
  • 财政年份:
    2023
  • 资助金额:
    $ 42.44万
  • 项目类别:
    Continuing Grant
Complex dynamics: group actions, Migdal-Kadanoff renormalization, and ergodic theory
复杂动力学:群作用、Migdal-Kadanoff 重整化和遍历理论
  • 批准号:
    2154414
  • 财政年份:
    2022
  • 资助金额:
    $ 42.44万
  • 项目类别:
    Standard Grant
Hyperbolic Dynamics in Physical Systems and Ergodic Theory
物理系统中的双曲动力学和遍历理论
  • 批准号:
    2154725
  • 财政年份:
    2022
  • 资助金额:
    $ 42.44万
  • 项目类别:
    Standard Grant
Multiplicative Ergodic Theory, Dynamics and Applications
乘法遍历理论、动力学和应用
  • 批准号:
    RGPIN-2018-03761
  • 财政年份:
    2022
  • 资助金额:
    $ 42.44万
  • 项目类别:
    Discovery Grants Program - Individual
New connections between Fractal Geometry, Harmonic Analysis and Ergodic Theory
分形几何、调和分析和遍历理论之间的新联系
  • 批准号:
    RGPIN-2020-04245
  • 财政年份:
    2022
  • 资助金额:
    $ 42.44万
  • 项目类别:
    Discovery Grants Program - Individual
Topics in Smooth Ergodic Theory: Stochastic Properties, Thermodynamic Formalism, Coexistence
平滑遍历理论主题:随机性质、热力学形式主义、共存
  • 批准号:
    2153053
  • 财政年份:
    2022
  • 资助金额:
    $ 42.44万
  • 项目类别:
    Standard Grant
Ergodic theory of low-dimensional dynamical systems
低维动力系统的遍历理论
  • 批准号:
    RGPIN-2017-06521
  • 财政年份:
    2022
  • 资助金额:
    $ 42.44万
  • 项目类别:
    Discovery Grants Program - Individual
Qualitative asymptotic problems in ergodic theory and probability
遍历理论和概率中的定性渐近问题
  • 批准号:
    RGPIN-2022-05066
  • 财政年份:
    2022
  • 资助金额:
    $ 42.44万
  • 项目类别:
    Discovery Grants Program - Individual
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了