World's Best Scientists 2026 revealed!

D-Index & Metrics

Mathematics

D-Index
41
Citations
5757
World Ranking
1940
National Ranking
33

Artur Avila publication distribution in Mathematics in 2026

The chart shows the distribution of publications by all Research.com ranked scientists in the field of Mathematics in 2026. The highlighted bar marks where Artur Avila sits on this spectrum.

42–46 publications: 3 scientists 47–51 publications: 5 scientists 52–56 publications: 7 scientists 57–61 publications: 20 scientists 62–66 publications: 14 scientists 67–71 publications: 25 scientists 72–76 publications: 19 scientists 77–81 publications: 35 scientists 82–86 publications: 50 scientists 87–91 publications: 60 scientists 92–96 publications: 86 scientists 97–101 publications: 84 scientists 102–106 publications: 83 scientists 107–111 publications: 90 scientists 112–116 publications: 99 scientists 117–121 publications: 90 scientists 122–126 publications: 91 scientists 127–131 publications: 109 scientists 132–136 publications: 110 scientists 137–141 publications: 98 scientists 142–146 publications: 112 scientists 147–151 publications: 102 scientists 152–156 publications: 88 scientists 157–161 publications: 106 scientists 162–166 publications: 83 scientists 167–171 publications: 102 scientists 172–176 publications: 77 scientists 177–181 publications: 81 scientists 182–186 publications: 78 scientists 187–191 publications: 71 scientists 192–196 publications: 92 scientists 197–201 publications: 64 scientists 202–206 publications: 69 scientists 207–211 publications: 64 scientists 212–216 publications: 62 scientists 217–221 publications: 58 scientists 222–226 publications: 53 scientists 227–231 publications: 50 scientists 232–236 publications: 46 scientists 237–241 publications: 46 scientists 242–246 publications: 46 scientists 247–251 publications: 43 scientists 252–256 publications: 29 scientists 257–261 publications: 45 scientists 262–266 publications: 30 scientists 267–271 publications: 33 scientists 272–276 publications: 34 scientists 277–281 publications: 30 scientists 282–286 publications: 31 scientists 287–291 publications: 21 scientists 292–296 publications: 34 scientists 297–301 publications: 26 scientists 302–306 publications: 10 scientists 307–311 publications: 17 scientists 312–316 publications: 23 scientists 317–321 publications: 13 scientists 322–326 publications: 16 scientists 327–331 publications: 26 scientists 332–336 publications: 13 scientists 337–341 publications: 13 scientists 342–346 publications: 16 scientists 347–351 publications: 17 scientists 352–356 publications: 12 scientists 357–361 publications: 18 scientists 362–366 publications: 18 scientists 367–371 publications: 9 scientists 372–376 publications: 11 scientists 377–381 publications: 8 scientists 382–386 publications: 8 scientists 387–391 publications: 9 scientists 392–396 publications: 9 scientists 397–401 publications: 8 scientists 402–406 publications: 11 scientists 407–411 publications: 6 scientists 412–416 publications: 6 scientists 417–421 publications: 9 scientists 422–426 publications: 8 scientists 427–431 publications: 5 scientists 432–436 publications: 8 scientists 437–441 publications: 8 scientists 442–446 publications: 4 scientists 447–451 publications: 4 scientists 452–456 publications: 4 scientists 457–461 publications: 2 scientists 462–466 publications: 2 scientists 467–471 publications: 4 scientists 472–476 publications: 3 scientists 477–481 publications: 3 scientists 482–486 publications: 6 scientists 487–491 publications: 3 scientists 492–496 publications: 5 scientists 497–501 publications: 5 scientists 502–506 publications: 1 scientists 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientists 522–526 publications: 3 scientists 527–531 publications: 1 scientists 532–536 publications: 4 scientists 537+ publications: 100 scientists
42 publications 537+

This scientist: 126 publications — 24th percentile

24% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 537 publications or more.

Artur Avila D-index placement in Mathematics in 2026

The chart shows the D-index (discipline H-index) distribution of Mathematics scientists ranked by Research.com in 2026. The highlighted bar marks where Artur Avila sits on this spectrum.

30 D-Index: 174 scientists 31 D-Index: 151 scientists 32 D-Index: 174 scientists 33 D-Index: 117 scientists 34 D-Index: 136 scientists 35 D-Index: 127 scientists 36 D-Index: 145 scientists 37 D-Index: 153 scientists 38 D-Index: 150 scientists 39 D-Index: 150 scientists 40 D-Index: 138 scientists 41 D-Index: 136 scientists 42 D-Index: 93 scientists 43 D-Index: 108 scientists 44 D-Index: 115 scientists 45 D-Index: 112 scientists 46 D-Index: 103 scientists 47 D-Index: 75 scientists 48 D-Index: 59 scientists 49 D-Index: 67 scientists 50 D-Index: 60 scientists 51 D-Index: 57 scientists 52 D-Index: 59 scientists 53 D-Index: 62 scientists 54 D-Index: 60 scientists 55 D-Index: 50 scientists 56 D-Index: 42 scientists 57 D-Index: 54 scientists 58 D-Index: 50 scientists 59 D-Index: 42 scientists 60 D-Index: 41 scientists 61 D-Index: 35 scientists 62 D-Index: 40 scientists 63 D-Index: 21 scientists 64 D-Index: 31 scientists 65 D-Index: 27 scientists 66 D-Index: 29 scientists 67 D-Index: 19 scientists 68 D-Index: 25 scientists 69 D-Index: 17 scientists 70 D-Index: 18 scientists 71 D-Index: 12 scientists 72 D-Index: 14 scientists 73 D-Index: 13 scientists 74 D-Index: 18 scientists 75 D-Index: 9 scientists 76 D-Index: 11 scientists 77 D-Index: 10 scientists 78 D-Index: 9 scientists 79 D-Index: 16 scientists 80 D-Index: 12 scientists 81 D-Index: 10 scientists 82 D-Index: 5 scientists 83 D-Index: 5 scientists 84 D-Index: 13 scientists 85 D-Index: 6 scientists 86+ D-Index: 99 scientists
30 D-Index 86+

This scientist: 41 D-Index — 49th percentile

49% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 86 D-Index or more.

Research.com Recognitions

  • 2019 - Member of the National Academy of Sciences
  • 2014 - Fields Medal of International Mathematical Union (IMU) For his profound contributions to dynamical systems theory, which have changed the face of the field, using the powerful idea of renormalization as a unifying principle.

Overview

Artur Avila is affiliated with the University of Zurich in Switzerland. Their research spans several areas within mathematics and physics, with a focus on mathematical physics and dynamical systems.

The main fields of study represented in their work include:

  • Mathematics
  • Physics and Astronomy

Within these fields, Avila's research contributions cover subfields such as:

  • Mathematical Physics
  • Statistical and Nonlinear Physics
  • Geometry and Topology
  • Applied Mathematics
  • Computational Theory and Mathematics

The topics most frequently addressed in their publications are:

  • Quantum chaos and dynamical systems
  • Spectral Theory in Mathematical Physics
  • Mathematical Dynamics and Fractals
  • Advanced Mathematical Modeling in Engineering
  • Numerical methods in inverse problems
  • Holomorphic and Operator Theory
  • Geometric and Algebraic Topology

Avila's published papers have appeared in a variety of venues, including:

  • arXiv (Cornell University)
  • Geometric and Functional Analysis
  • Astérisque
  • Duke Mathematical Journal
  • Annals of Mathematics

Recent notable papers include:

  • "Lebesgue measure of Feigenbaum Julia sets" (2022) in Annals of Mathematics
  • "On the abominable properties of the almost Mathieu operator with well-approximated frequencies" (2024) in Duke Mathematical Journal
  • "Schrödinger operators with potentials generated by hyperbolic transformations: I-positivity of the Lyapunov exponent" (2022) in Inventiones mathematicae
  • "Quantitative weak mixing for interval exchange transformations" (2023) in Geometric and Functional Analysis
  • "Mixing for smooth time-changes of general nilflows" (2021) in Advances in Mathematics

Frequent co-authors with whom Avila has collaborated include:

  • David Damanik
  • Zhenghe Zhang
  • Giovanni Forni
  • Yoram Last
  • Mira Shamis

Avila has received recognition in their field, notably being awarded the Fields Medal by the International Mathematical Union in 2014, cited for contributions to dynamical systems theory through the use of renormalization as a unifying principle.

Additionally, Avila was elected as a Member of the National Academy of Sciences in 2019.

Best Publications

  • The Ten Martini Problem

    Artur Avila;Svetlanaya Jitomirskaya

  • Weak mixing for interval exchange transformations and translation flows

    Artur Avila;Giovanni Forni

  • Reducibility or nonuniform hyperbolicity for quasiperiodic Schrodinger cocycles

    Artur Ávila;Raphaël Krikorian

  • Global theory of one-frequency Schrödinger operators

    Artur Avila;Artur Avila

  • Exponential mixing for the Teichmüller flow

    Artur Avila;Sébastien Gouëzel;Jean-Christophe Yoccoz

  • Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture

    Artur Avila;Marcelo Viana

  • Almost localization and almost reducibility

    Artur Avila;Svetlanaya Jitomirskaya

  • Extremal Lyapunov exponents: an invariance principle and applications

    Artur Avila;Artur Avila;Marcelo Viana

  • Sharp phase transitions for the almost Mathieu operator

    Artur Avila;Jiangong You;Qi Zhou

  • A KAM SCHEME FOR SL(2, R) COCYCLES WITH LIOUVILLEAN FREQUENCIES

    Artur Avila;Bassam Fayad;Raphaël Krikorian

  • Regular or stochastic dynamics in real analytic families of unimodal maps

    Artur Avila;Mikhail Lyubich;Mikhail Lyubich;Welington de Melo

  • Almost reducibility and absolute continuity I

    Artur Avila

  • On the regularization of conservative maps

    Artur Avila;Artur Avila

  • The absolutely continuous spectrum of the almost Mathieu operator

    Artur Avila

  • Statistical properties of unimodal maps: the quadratic family

    Artur Ávila;Carlos Gustavo Moreira

  • Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows

    Artur Avila;Marcelo Viana;Amie Wilkinson

  • Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling

    Artur Avila;David Damanik

  • On the Spectrum and Lyapunov Exponent of Limit Periodic Schrödinger Operators

    Artur Avila;Artur Avila

  • An integrable deformation of an ellipse of small eccentricity is an ellipse

    Artur Avila;Jacopo De Simoi;Vadim Kaloshin

  • Complex one-frequency cocycles

    Artur Avila;Svetlana Jitomirskaya;Christian Sadel

  • Spectral theory of extended Harper’s model and a question by Erdős and Szekeres

    A. Avila;S. Jitomirskaya;C. A. Marx

Frequent Co-Authors

Svetlana Jitomirskaya
Svetlana Jitomirskaya University of California, Irvine
David Damanik
David Damanik Rice University
Marcelo Viana
Marcelo Viana Instituto Nacional de Matemática Pura e Aplicada
Barry Simon
Barry Simon California Institute of Technology
Alex Eskin
Alex Eskin University of Chicago
Eduard Looijenga
Eduard Looijenga Utrecht University
Fritz Grunewald
Fritz Grunewald Heinrich Heine University Düsseldorf
John Coates
John Coates University of Cambridge

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