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Abundance of counterexamples to the finiteness conjecture in arbitrary dimension (working title)

Çağrı Sert


In progress...


Extremal norms for fiber bunched cocycles

Eduardo Garibaldi




Emergence and complexity of the set of invariant measures (working title)

Pierre Berger


In progress...


Ergodic optimization of Birkhoff averages and Lyapunov exponents




Proceedings of the International Congress of Mathematicians 2018, Rio de Janeiro, vol. 2, pp. 18211842.

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Equilibrium states of generalised singular value potentials and applications to affine iterated function systems

Ian D. Morris


Geometric and Functional Analysis, 28 (2018), no. 4, pp. 9951028.

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Dominated Pesin theory: convex sum of hyperbolic measures

Christian Bonatti,
Katrin Gelfert


Israel Journal of Mathematics, 226 (2018), no. 1, pp. 387417.

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On the approximation of convex bodies by ellipses with respect to the symmetric difference metric




Discrete & Computational Geometry, 60 (2018), no. 4, pp. 938966.

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Positivity of the top Lyapunov exponent for cocycles on semisimple Lie groups over hyperbolic bases

M. Bessa,
M. Cambrainha,
C. Matheus,
P. Varandas,
Disheng Xu


Bulletin of the Brazilian Mathematical Society, 49 (2018), no. 1, pp. 7387.

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A criterion for zero averages and full support of ergodic measures

Christian Bonatti,
Lorenzo J. Díaz


Moscow Mathematical Journal, 18 (2018), no. 1, pp. 1561.

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Anosov representations and dominated splittings

Rafael Potrie, Andrés Sambarino


To appear in Journal of the European Mathematical Society


Flexibility of Lyapunov exponents among conservative diffeormophisms (working title)

Anatole Katok,
Federico Rodriguez Hertz


In progress...


Robust criterion for the existence of nonhyperbolic measures

Christian Bonatti,
Lorenzo J. Díaz


Communications in Mathematical Physics 344 (2016), no. 3, pp. 751795.

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The scaling mean and a law of large permanents

Godofredo Iommi,
Mario Ponce


Advances in Mathematics 292 (2016), pp. 374409.

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Ergodic optimization of prevalent supercontinuous functions

Yiwei Zhang


International Mathematics Research Notices 2016 (2016), no. 19, pp. 59886017.

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Cocycles of isometries and denseness of domination




Quarterly Journal of Mathematics 66 (2015), no. 3, pp. 773798.

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Peano curves with smooth footprints

Pedro H. Milet


Monatshefte für Mathematik 180 (2016), no. 4, pp. 693712.

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The entropy of Lyapunovoptimizing measures of some matrix cocycles

Michał Rams


Journal of Modern Dynamics 10 (2016), pp. 255286.

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Continuity properties of the lower spectral radius

Ian D. Morris


Proceedings of the London Mathematical Society 110 (2015), pp. 477509.

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Generic linear cocycles over a minimal base




Studia Mathematica 218 (2013), no. 2, pp. 167188.

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Almost reduction and perturbation of matrix cocycles

Andrés Navas


Annales de l'Institut Henri Poincaré  analyse non linéaire 31 (2014), no. 6, pp. 11011107.

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Robust vanishing of all Lyapunov exponents for iterated function systems

Christian Bonatti,
Lorenzo J. Díaz


Mathematische Zeitschrift 176 (2014), pp. 469503.

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Universal regular control for generic semilinear systems

Nicolas Gourmelon


Mathematics of Control, Signals, and Systems 26 (2014), no. 4, pp. 481518.

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A geometric path from zero Lyapunov exponents to rotation cocycles

Andrés Navas


Ergodic Theory and Dynamical Systems 35 (2015), no. 2, pp. 374402.

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Perturbation of the Lyapunov spectra of periodic orbits

Christian Bonatti


Proceedings of the London Mathematical Society 105 (2012), no. 1, pp. 148.

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Nonuniform hyperbolicity, global dominated splittings and generic properties of volumepreserving diffeomorphisms

Artur Avila


Transactions of the American Mathematical Society 364 (2012), no. 6, pp. 28832907.

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Opening gaps in the spectrum of strictly ergodic Schrödinger operators

Artur Avila, David Damanik


Journal of the European Mathematical Society 14 (2012), no. 1, pp. 61106.

/ Correction:

Nonuniform center bunching and the genericity of ergodicity among \(C^1\) partially hyperbolic symplectomorphisms

Artur Avila, Amie Wilkinson


Annales Scientifiques de l'École Normale Supérieure 42 (2009), no. 6, pp. 931979.

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Some characterizations of domination

Nicolas Gourmelon


Mathematische Zeitschrift 263 (2009), no. 1, pp. 221231.

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Uniformly hyperbolic finitevalued \({\rm SL}(2,\Bbb{R})\) cocycles

Artur Avila, JeanChristophe Yoccoz


Commentarii Mathematici Helvetici 85 (2010), no. 4, pp. 813884.

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\(C^1\)generic symplectic diffeomorphisms: partial hyperbolicity and zero centre Lyapunov exponents




Journal of the Institute of Mathematics of Jussieu, 9 (2010), no. 1, pp. 4993.

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Cantor spectrum for Schrödinger operators with potentials arising from generalized skewshifts

Artur Avila, David Damanik


Duke Mathematical Journal 146 (2009), no. 2, pp. 253280.

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A uniform dichotomy for generic \({\rm SL}(2,\Bbb{R})\) cocycles over a minimal base

Artur Avila


Bulletin de la Société Mathématique de France 135 (2007), 407417.

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Generic expanding maps without absolutely continuous invariant \(\sigma\)finite measure

Artur Avila


Mathematical Research Letters 14 (2007), no. 5, 721730.

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A generic \(C^1\) map has no absolutely continuous invariant probability measure

Artur Avila


Nonlinearity 19 (2006), 27172725.

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Dichotomies between uniform hyperbolicity and zero Lyapunov exponents for \({\rm SL}(2,\Bbb{R})\) cocycles

Bassam Fayad


Bulletin of the Brazilian Mathematical Society 37 (2006), no. 3, 307349.

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A remark on conservative diffeomorphisms

Bassam Fayad, Enrique Pujals


Comptes Rendus Acad. Sci. Paris, Ser. I 342 (2006), 763766.

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\(L^p\)generic cocycles have onepoint Lyapunov spectrum

Alexander Arbieto


Stochastics and Dynamics 3 (2003), 7381. Corrigendum. ibid, 3 (2003), 419420.

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Lyapunov exponents: How frequently are dynamical systems hyperbolic?

Marcelo Viana


Modern dynamical systems and applications, 271297, Brin, Hasselblatt, Pesin (eds.) Cambridge Univ. Press, 2004.

Correction:

Inequalities for numerical invariants of sets of matrices




Linear Algebra and its Applications, 368 (2003), 7181.

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The Lyapunov exponents of generic volume preserving and symplectic maps

Marcelo Viana


Annals of Mathematics, 161 (2005), no. 3, 14231485.

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Robust transitivity and topological mixing for \(C^1\)flows

Flavio Abdenur, Artur Avila


Proceedings of American Mathematical Society, 132 (2004), 699705.

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Uniform (projective) hyperbolicity or no hyperbolicity: a dichotomy for generic conservative maps

Marcelo Viana


Annales de l'Institut Henri Poincaré  analyse non linéaire, 19 (2002), 113123.

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A formula with some applications to the theory of Lyapunov exponents

Artur Avila


Israel Journal of Mathematics, 131 (2002), 125137.

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Genericity of zero Lyapunov exponents




Ergodic Theory and Dynamical Systems, 22 (2002), 16671696.

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Discontinuity of the Lyapunov exponent for nonhyperbolic cocycles




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