Carlos Matheus

Carlos Matheus's AcademicInfluence.com Rankings

Carlos Matheus

Mathematics

#5319

World Rank

#7494

Historical Rank

Measure Theory

#5095

World Rank

#6026

Historical Rank

mathematics Degrees

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Mathematics

Why Is Carlos Matheus Influential?

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According to Wikipedia, Carlos Matheus Silva Santos is a Brazilian mathematician working in dynamical systems, analysis and geometry. He currently works at the CNRS, in Paris. He earned his Ph.D. from the Instituto de Matemática Pura e Aplicada in 2004 under the supervision of Marcelo Viana, at the age of 19.

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Carlos Matheus's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Introduction to Teichm\"uller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards (2013) (87)
SQUARE-TILED CYCLIC COVERS (2010) (52)
A criterion for the simplicity of the Lyapunov spectrum of square-tiled surfaces (2013) (42)
Lyapunov spectrum of invariant subbundles of the Hodge bundle (2011) (40)
A pasting lemma and some applications for conservative systems (2006) (36)
The action of the affine diffeomorphisms on the relative homology group of certain exceptionally symmetric origamis (2009) (36)
AN EXAMPLE OF A TEICHMÜLLER DISK IN GENUS 4 WITH DEGENERATE KONTSEVICH-ZORICH SPECTRUM (2008) (33)
Well posedness for the 1D Zakharov-Rubenchik system (2008) (31)
Abundance of stable ergodicity (2004) (30)
Hodge–Teichmüller planes and finiteness results for Teichmüller curves (2015) (29)
Equilibrium states for random non-uniformly expanding maps (2003) (28)
Zero Lyapunov exponents of the Hodge bundle (2012) (27)
Symbolic dynamics for non-uniformly hyperbolic surface maps with discontinuities (2016) (26)
Fast decay of correlations of equilibrium states of open classes of non-uniformly expanding maps and potentials (2006) (18)
Homology of origamis with symmetries (2012) (17)
A coding-free simplicity criterion for the Lyapunov exponents of Teichmüller curves (2012) (17)
Rough solutions for the periodic Schrödinger–Korteweg–de Vries system (2005) (15)
Rates of mixing for the Weil–Petersson geodesic flow: exponential mixing in exceptional moduli Spaces (2016) (14)
Global Well-Posedness and Non-linear Stability of Periodic Traveling Waves for a Schrodinger-Benjamin-Ono System (2007) (13)
Zorich conjecture for hyperelliptic Rauzy–Veech groups (2016) (11)
Fractal geometry of the complement of Lagrange spectrum in Markov spectrum (2018) (11)
Quaternionic covers and monodromy of the Kontsevich-Zorich cocycle in orthogonal groups (2015) (10)
$${SL(2, \mathbb{R})}$$SL(2,R) -invariant probability measures on the moduli spaces of translation surfaces are regular (2013) (10)
Hodge-Teichmueller planes and finiteness results for Teichmueller curves (2013) (9)
The Lagrange and Markov Spectra from the Dynamical Point of View (2017) (9)
Some quantitative versions of Ratner’s mixing estimates (2013) (9)
Rates of mixing for the Weil-Petersson geodesic flow I: no rapid mixing in non-exceptional moduli spaces (2013) (9)
Classical and Dynamical Markov and Lagrange Spectra (2020) (9)
Lower bounds on the dimension of the Rauzy gasket (2019) (8)
The remarkable effectiveness of ergodic theory in number theory (2009) (8)
Markov spectrum near Freiman's isolated points in M ∖ L (2019) (8)
Sharp bilinear estimates and well-posedness for the 1-D Schrödinger-Debye system (2006) (8)
Decidability of Chaos for Some Families of Dynamical Systems (2002) (8)
A Pasting Lemma I: the case of vector fields (2003) (6)
Maximal entropy measures for Viana maps (2003) (5)
Explicit Teichmüller curves with complementary series (2013) (5)
On the periodic Schrodinger-Debye equation (2005) (5)
Positivity of the Top Lyapunov Exponent for Cocycles on Semisimple Lie Groups over Hyperbolic Bases (2016) (5)
Lecture notes on the dynamics of the Weil-Petersson flow (2016) (4)
On special Lagrangian fibrations in generic twistor families of K3 surfaces (2017) (4)
Cohomological equation and local conjugacy class of Diophantine interval exchange maps (2017) (4)
THREE LECTURES ON SQUARE-TILED SURFACES (2018) (4)
The Kontsevich–Zorich cocycle over Veech–McMullen family of symmetric translation surfaces (2017) (4)
The Bernoulli Property for Weakly Hyperbolic Systems (2004) (4)
Axiom A versus Newhouse phenomena for Benedicks-Carleson toy models (2010) (3)
The Teichmüller geodesic flow and the geometry of the Hodge bundle@@@Le flot géodésique de Teichmüller et la géométrie du fibré de Hodge (2010) (3)
Hausdorff dimension of Gauss–Cantor sets and two applications to classical Lagrange and Markov spectra (2021) (3)
Markov spectrum near Freiman's isolated points in $M\setminus L$ (2018) (3)
Approximation of the Lagrange and Markov spectra (2019) (2)
Some Examples of Isotropic SL(2, ℝ)-Invariant Subbundles of the Hodge Bundle (2013) (2)
A criterion for the simplicity of the Lyapunov spectrum of square-tiled surfaces (2014) (2)
Polynomial decay of correlations for nonpositively curved surfaces (2021) (2)
Explicit Teichm\"uller curves with complemetary series (2011) (2)
Typical symplectic locally constant cocycles over certain shifts of countable type have simple Lyapunov spectra (2016) (2)
Non-uniformly hyperbolic horseshoes in the standard family (2017) (2)
geometrical versus topological properties of manifolds (2003) (2)
Cusp excursions of random geodesics in Weil–Petersson type metrics (2017) (1)
Diophantine Approximation, Lagrange and Markov Spectra, and Dynamical Cantor Sets (2021) (1)
ON THE PERIODIC SCHR ¨ ODINGER-DEBYE EQUATION (2005) (1)
Geometrical versus Topological Properties of Manifolds and a Remark on Poincar\'e Conjecture (2003) (1)
The Dynamics of the Weil–Petersson Flow (2017) (1)
Semisimplicity of the Lyapunov spectrum for irreducible cocycles (2013) (1)
Rates of mixing of Weil-Pertesson geodesic flows (2013) (1)
An estimate on the Hausdorff dimension of stable sets of non-uniformly hyperbolic horseshoes (2017) (1)
Corrigendum to “Homology of origamis with symmetries” (2016) (1)
Arithmeticity of the Kontsevich--Zorich monodromies of certain families of square-tiled surfaces II (2022) (1)
$M\setminus L$ near 3 (2019) (1)
A P ] 2 6 Ja n 20 07 Global Well-Posedness and Non-linear Stability of Periodic Travelling Waves Solutions for a Schrödinger-Benjamin-Ono System (2007) (1)
Ergodicity of geodesic flows on incomplete negatively curved manifolds (2017) (1)
A P ] 2 5 N ov 2 00 5 On the periodic Schrödinger-Debye equation (2008) (0)
FRACTAL GEOMETRY OF NON-UNIFORMLY HYPERBOLIC HORSESHOES (2013) (0)
Non-planarity of $\text{SL}(2,\mathbb{Z})$-orbits of origamis in $\mathcal{H}(2)$ (2021) (0)
Non-linear bi-algebraic curves and surfaces in moduli spaces of Abelian differentials (2023) (0)
The beginning of the Lagrange spectrum of certain origamis of genus two (2020) (0)
STABLE SETS OF CERTAIN NON-UNIFORMLY HYPERBOLIC HORSESHOES HAVE THE EXPECTED DIMENSION (2017) (0)
A remark on capillary surfaces in a 3-dimensional space of constant curvature (2003) (0)
Rates of mixing for the Weil–Petersson geodesic flow: exponential mixing in exceptional moduli Spaces (2017) (0)
Non-ergodicity on SU(2) and SU(3) character varieties of the once-punctured torus (2022) (0)
New gaps on the Lagrange and Markov spectra (2022) (0)
Some quantitative versions of Ratner’s mixing estimates (2013) (0)
Global well-posedness for a NLS-KdV system on $\mathbb{T}$ (2005) (0)
On the graph of the dimension function of the Lagrange and Markov spectra (2022) (0)
Zorich conjecture for hyperelliptic Rauzy–Veech groups (2017) (0)
Some Variants of Orponen’s Theorem on Visible Parts of Fractal Sets (2020) (0)
GLOBAL WELL-POSEDNESS OF NLS-KDV SYSTEMS FOR PERIODIC FUNCTIONS (2006) (0)
$M\backslash L$ is not closed (2019) (0)
Positivity of the Top Lyapunov Exponent for Cocycles on Semisimple Lie Groups over Hyperbolic Bases (2017) (0)
Diophantine approximations, Markov and Lagrange spectra and dynamical Cantor sets (2021) (0)
M ∖ L Near 3 (2021) (0)
J ul 2 00 3 Geometrical versus Topological Properties of Manifolds and a Remark on Poincaré Conjecture (2002) (0)
Appendix D Variations of Hodge structures , Lyapunov exponents and Kontsevich ’ s formula (2016) (0)
A coding-free simplicity criterion for the Lyapunov exponents of Teichmüller curves (2015) (0)
D G ] 1 9 N ov 2 00 5 Geometrical versus Topological Properties of Manifolds (2003) (0)
Immersions with fractal set of points of zero Gauss-Kronecker curvature (2003) (0)
New numbers in $M\setminus L$ beyond $\sqrt{12}$: solution to a conjecture of Cusick (2018) (0)
On the dynamics on the SU(2)-character variety of a once-punctured torus (2021) (0)
Semisimplicity of the Lyapunov spectrum for irreducible cocycles (2019) (0)
GLOBAL WELL-POSEDNESS FOR A NLS-KDV SYSTEM ON T (2005) (0)
M∖L is Not Closed (2020) (0)
C. Matheus - Square tiled surfaces (Part 2) (2018) (0)

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What Schools Are Affiliated With Carlos Matheus?

Carlos Matheus is affiliated with the following schools:

Polytechnic Institute of Paris