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- Artur Avila

Mathematics

Brazil

2022

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
34
Citations
4,582
122
World Ranking
2064
National Ranking
38

2022 - Research.com Mathematics in Brazil Leader Award

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.

- Mathematical analysis
- Geometry
- Algebra

Artur Avila spends much of his time researching Mathematical analysis, Spectrum, Lyapunov exponent, Pure mathematics and Absolute continuity. The various areas that he examines in his Mathematical analysis study include Translation surface and Rigidity. His studies in Spectrum integrate themes in fields like Phase transition and Mathematical physics.

His study in Pure mathematics is interdisciplinary in nature, drawing from both Measure and Constant. His work in Absolute continuity addresses issues such as Discrete mathematics, which are connected to fields such as Stochastic dynamics, Space and Invariant measure. His Ergodic theory study combines topics in areas such as Dynamical system and Calculus.

- The Ten Martini Problem (264 citations)
- Weak mixing for interval exchange transformations and translation flows (163 citations)
- Almost localization and almost reducibility (143 citations)

Artur Avila mainly investigates Pure mathematics, Mathematical analysis, Lyapunov exponent, Ergodic theory and Conjecture. His Pure mathematics research is multidisciplinary, incorporating elements of Mixing and Exponential function. His work deals with themes such as Novikov self-consistency principle, Invariant measure, Spectrum and Parameter space, which intersect with Mathematical analysis.

His study in the field of Lyapunov equation is also linked to topics like Open set, Spectral radius, Codimension and Dynamical systems theory. His Ergodic theory research includes themes of Discrete mathematics, Countable set, Quadratic equation, Schrödinger's cat and Ergodicity. His work carried out in the field of Conjecture brings together such families of science as Structure and Closure.

- Pure mathematics (70.85%)
- Mathematical analysis (37.69%)
- Lyapunov exponent (29.65%)

- Pure mathematics (70.85%)
- Diffeomorphism (9.55%)
- Conjecture (24.12%)

Artur Avila mostly deals with Pure mathematics, Diffeomorphism, Conjecture, Ergodic theory and Irrational number. His Pure mathematics research includes elements of Entropy, Fixed point and Mixing. His work in Diffeomorphism covers topics such as Closed manifold which are related to areas like Geometry and topology and Discrete mathematics.

His research in Conjecture intersects with topics in Structure, Closure and Phase. Artur Avila merges Ergodic theory with Lyapunov exponent in his study. His work on Irrational rotation as part of general Irrational number study is frequently linked to Alpha, therefore connecting diverse disciplines of science.

- Sharp phase transitions for the almost Mathieu operator (51 citations)
- Symplectic and isometric SL(2,#x211D;)-invariant subbundles of the Hodge bundle (19 citations)
- Spectral theory of extended Harper’s model and a question by Erdős and Szekeres (18 citations)

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

The Ten Martini Problem

Artur Avila;Svetlanaya Jitomirskaya.

Annals of Mathematics **(2009)**

335 Citations

The Ten Martini Problem

Artur Avila;Svetlanaya Jitomirskaya.

Annals of Mathematics **(2009)**

335 Citations

Weak mixing for interval exchange transformations and translation flows

Artur Avila;Giovanni Forni.

Annals of Mathematics **(2007)**

228 Citations

Weak mixing for interval exchange transformations and translation flows

Artur Avila;Giovanni Forni.

Annals of Mathematics **(2007)**

228 Citations

Reducibility or nonuniform hyperbolicity for quasiperiodic Schrodinger cocycles

Artur Ávila;Raphaël Krikorian.

Annals of Mathematics **(2006)**

218 Citations

Reducibility or nonuniform hyperbolicity for quasiperiodic Schrodinger cocycles

Artur Ávila;Raphaël Krikorian.

Annals of Mathematics **(2006)**

218 Citations

Exponential mixing for the Teichmüller flow

Artur Avila;Sébastien Gouëzel;Jean-Christophe Yoccoz.

Publications Mathématiques de l'IHÉS **(2006)**

204 Citations

Exponential mixing for the Teichmüller flow

Artur Avila;Sébastien Gouëzel;Jean-Christophe Yoccoz.

Publications Mathématiques de l'IHÉS **(2006)**

204 Citations

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

Artur Avila;Marcelo Viana.

Acta Mathematica **(2007)**

191 Citations

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

Artur Avila;Marcelo Viana.

Acta Mathematica **(2007)**

191 Citations

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