Artur Avila

3.1k total citations · 1 hit paper
60 papers, 1.2k citations indexed

About

Artur Avila is a scholar working on Mathematical Physics, Statistical and Nonlinear Physics and Geometry and Topology. According to data from OpenAlex, Artur Avila has authored 60 papers receiving a total of 1.2k indexed citations (citations by other indexed papers that have themselves been cited), including 58 papers in Mathematical Physics, 34 papers in Statistical and Nonlinear Physics and 27 papers in Geometry and Topology. Recurrent topics in Artur Avila's work include Mathematical Dynamics and Fractals (40 papers), Quantum chaos and dynamical systems (32 papers) and Spectral Theory in Mathematical Physics (14 papers). Artur Avila is often cited by papers focused on Mathematical Dynamics and Fractals (40 papers), Quantum chaos and dynamical systems (32 papers) and Spectral Theory in Mathematical Physics (14 papers). Artur Avila collaborates with scholars based in France, Brazil and United States. Artur Avila's co-authors include Svetlana Jitomirskaya, Marcelo Viana, Mikhail Lyubich, Sébastien Gouëzel, Raphaël Krikorian, Bassam Fayad, Jean-Christophe Yoccoz, Jairo Bochi, Welington de Melo and Pascal Hubert and has published in prestigious journals such as Communications in Mathematical Physics, Annals of Mathematics and Inventiones mathematicae.

In The Last Decade

Artur Avila

56 papers receiving 1.1k citations

Hit Papers

align trajectories

What are hit papers?

Hit papers significantly outperform the citation benchmark for their cohort. A paper qualifies if it has ≥500 total citations, achieves ≥1.5× the top-1% citation threshold for papers in the same subfield and year (this is the minimum needed to enter the top 1%, not the average within it), or reaches the top citation threshold in at least one of its specific research topics.

The Ten Martini Problem

2009 184 citations Artur Avila, Svetlana Jitomirskaya Annals of Mathematics profile →

Peers

Artur Avila

MP

SNP

GT

AMPO

CTM

Svetlana Jitomirskaya United States

Jiangong You China

David Damanik United States

Yoram Last Israel

L. H. Eliasson Sweden

Michael R. Herman France

Pierre Moussa France

Boris Mityagin United States

Artur O. Lopes Brazil

Alexander Teplyaev United States

Svetlana Jitomirskaya United States

Artur Avila

1.3k ×1.2

MP

772 ×1.1

SNP

103 ×0.3

GT

523 ×2.2

AMPO

426 ×2.0

CTM

Citations per year, relative to Artur Avila Artur Avila (= 1×) peers Svetlana Jitomirskaya

Countries citing papers authored by Artur Avila

Since Specialization

Citations

This map shows the geographic impact of Artur Avila's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Artur Avila with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Artur Avila more than expected).

Fields of papers citing papers by Artur Avila

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Artur Avila. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Artur Avila. The network helps show where Artur Avila may publish in the future.

Co-authorship network of co-authors of Artur Avila

This figure shows the co-authorship network connecting the top 25 collaborators of Artur Avila. A scholar is included among the top collaborators of Artur Avila based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Artur Avila. Artur Avila is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

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20 of 20 papers shown

1.

Avila, Artur, David Damanik, & Anton Gorodetski. (2023). The Spectrum of Schrödinger Operators with Randomly Perturbed Ergodic Potentials. Geometric and Functional Analysis. 33(2). 364–375. 2 indexed citations

2.

Avila, Artur & Bassam Fayad. (2021). Non-differentiable irrational curves for twist map. Ergodic Theory and Dynamical Systems. 42(2). 491–499.

3.

Avila, Artur, et al.. (2019). On mixing diffeomorphisms of the disc. Inventiones mathematicae. 220(3). 673–714. 8 indexed citations

4.

Avila, Artur, et al.. (2018). Livšic theorem for diffeomorphism cocycles. Geometric and Functional Analysis. 28(4). 943–964. 4 indexed citations

5.

Avila, Artur, et al.. (2018). Cocycles over partially hyperbolic maps. Astérisque. 2 indexed citations

6.

Avila, Artur, Carlos Matheus, & Jean-Christophe Yoccoz. (2017). The Kontsevich--Zorich cocycle over Veech--McMullen family of symmetric\n translation surfaces. arXiv (Cornell University). 2 indexed citations

7.

Avila, Artur, Alex Eskin, & Martin Möller. (2015). Symplectic and isometric SL(2,#x211D;)-invariant subbundles of the Hodge bundle. Journal für die reine und angewandte Mathematik (Crelles Journal). 2017(732). 1–20. 15 indexed citations

8.

Avila, Artur. (2015). Global theory of one-frequency Schrödinger operators. Acta Mathematica. 215(1). 1–54. 118 indexed citations

9.

Avila, Artur, et al.. (2014). Complex one-frequency cocycles. Journal of the European Mathematical Society. 16(9). 1915–1935. 27 indexed citations

10.

Avila, Artur & Sébastien Gouëzel. (2013). Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow. Annals of Mathematics. 178(2). 385–442. 11 indexed citations

11.

Avila, Artur. (2013). On rigidity of critical circle maps. Bulletin of the Brazilian Mathematical Society New Series. 44(4). 611–619. 9 indexed citations

12.

Avila, Artur, et al.. (2012). Exponential mixing for the Teichmüller flow in the space of quadratic differentials. Commentarii Mathematici Helvetici. 87(3). 589–638. 7 indexed citations

13.

Avila, Artur, Giovanni Forni, & Corinna Ulcigrai. (2011). Mixing for the time-changes of Heisenberg nilflows. Journal of Differential Geometry. 89(3). 6 indexed citations

14.

Avila, Artur, Mikhail Lyubich, & Weixiao Shen. (2010). Parapuzzle of the multibrot set and typical dynamics of unimodal maps. Journal of the European Mathematical Society. 13(1). 27–56. 13 indexed citations

15.

Avila, Artur & Marcelo Viana. (2010). Extremal Lyapunov exponents: an invariance principle and applications. Inventiones mathematicae. 181(1). 115–178. 60 indexed citations

16.

Avila, Artur, et al.. (2009). Uniform exponential growth for some <em>SL(2, R)</em> matrix products. Journal of Modern Dynamics. 3(4). 549–554. 2 indexed citations

17.

Avila, Artur & Marcelo Viana. (2007). Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture. Acta Mathematica. 198(1). 1–56. 60 indexed citations

18.

Avila, Artur & Carlos Gustavo Moreira. (2004). Quasisymmetric robustness of the Collet-Eckmann condition in the quadratic family. Bulletin of the Brazilian Mathematical Society New Series. 35(2). 291–331.

19.

Avila, Artur, et al.. (2004). Siegel disks with smooth boundaries. Acta Mathematica. 193(1). 1–30. 23 indexed citations

20.

Avila, Artur. (2002). Bifurcations d'applications unimodales. Comptes Rendus Mathématique. 334(6). 483–488. 1 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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