Artur Avila

Mathematical Physics · 2000–2017

A researcher in the Science corpus: 32 papers; trusts 38 researchers and is trusted by 49 researchers here, as inferred from the citation graph.

Subfields

• Mathematical Physics — 154 citations into it; #196 of 8,562 by trust here, #106 by citations
• Statistical and Nonlinear Physics — 89 citations into it; #482 of 10,127 by trust here, #644 by citations
• Geometry and Topology — 69 citations into it; #561 of 7,422 by trust here, #494 by citations
• Applied Mathematics — 46 citations into it; #1,104 of 7,620 by trust here, #904 by citations
• Computational Theory and Mathematics — 20 citations into it
• Computer Networks and Communications — 10 citations into it; #7,913 of 9,886 by trust here, #6,498 by citations

Whom Artur Avila trusts overall

Their strongest outbound trust, strongest first, inferred from their citations.

1. Marcelo Viana
2. Jairo Bochi
3. C. Bonatti
4. Jean Bourgain
5. S. Jitomirskaya
6. G. Forni
7. Keith Burns
8. Amie Wilkinson
9. F. R. Hertz
10. Jayadev S. Athreya

Who trusts Artur Avila overall

1. A. Zorich
2. David Damanik
3. Marcelo Viana
4. Jiangong You
5. Jiagang Yang
6. G. Forni
7. Corentin Boissy
8. A. Eskin
9. Bassam Fayad
10. Qi Zhou

Papers from Artur Avila's perspective

Ordered by how strongly the researchers Artur Avila trusts endorse each paper. Same corpus, a different order for every researcher.

1. Pathological foliations and removable zero exponents
2. SRB measures for partially hyperbolic systems whose central direction is mostly expanding
3. GÉNÉRICITÉ D'EXPOSANTS DE LYAPUNOV NON-NULS POUR DES PRODUITS DÉTERMINISTES DE MATRICES GENERICITY OF NON-ZERO LYAPUNOV EXPONENTS FOR DETERMINISTIC PRODUCTS OF MATRICES
4. Extremal Lyapunov exponents: an invariance principle and applications
5. Recent Results About Stable Ergodicity
6. On differentiability of SRB states for partially hyperbolic systems
7. The Lyapunov exponents of generic volume-preserving and symplectic maps
8. Accessibility and stable ergodicity for partially hyperbolic diffeomorphisms with 1D-center bundle
9. Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents
10. Absolutely Singular Dynamical Foliations

Their papers

• C1 density of stable ergodicity (2017) — 65 citations
• Sharp phase transitions for the almost Mathieu operator (2015) — 152 citations
• Global theory of one-frequency Schrödinger operators (2015) — 287 citations
• An integrable deformation of an ellipse of small eccentricity is an ellipse (2014) — 98 citations
• Diffeomorphisms with positive metric entropy (2014) — 58 citations
• Diffusion for chaotic plane sections of 3-periodic surfaces (2014) — 55 citations
• Complex one-frequency cocycles (2013) — 82 citations
• On the Hausdorff dimension of the Rauzy gasket (2013) — 71 citations
• Monotonic cocycles (2013) — 51 citations
• Symplectic and Isometric SL(2,R) invariant subbundles of the Hodge bundle (2012) — 68 citations
• Absolute continuity, Lyapunov exponents and rigidity I : geodesic flows (2011) — 83 citations
• Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow (2010) — 60 citations
• The full renormalization horseshoe for unimodal maps of higher degree: exponential contraction along hybrid classes (2010) — 49 citations
• A Kam Scheme for SL(2, $${{\mathbb R}}$$) Cocycles with Liouvillean Frequencies (2010) — 89 citations
• Almost reducibility and absolute continuity I (2010) — 97 citations
• A KAM scheme for SL(2,R) cocycles with Liouvillean frequencies (2010) — 102 citations
• Extremal Lyapunov exponents: an invariance principle and applications (2010) — 187 citations
• The Ten Martini Problem (2009) — 384 citations
• On the regularization of conservative maps (2008) — 67 citations
• Uniformly Hyperbolic Finite-Valued SL(2,R)-Cocycles (2008) — 68 citations