Rafael Lucena, professor...and Olga's daddy

Welcome, I am Rafael Lucena, a tenured professor at the Institute of Mathematics at the Federal University of Alagoas, Brazil.

Here you can follow my work in pure mathematics research. My primary research focus is on Dynamical Systems and Ergodic Theory, with an emphasis on the statistical properties.

If you require further information, do not hesitate to reach out. You can find my contact details at the bottom of this page.

Para acessar a versão em Português, clique aqui.

Publications

[7] Statistical stability for systems semi-conjugate to pre-piecewise convex or expanding maps with countably many branches (preprint - work in progress)

[6] Quasi-compactness and statistical properties for discontinuous systems semi-conjugate to piecewise convex maps with countably many branches (article - Discrete and Continuous Dynamical Systems - Click here)

[5] Thermodynamic formalism for discontinuous maps and statistical properties for their equilibrium states (preprint - work in progress)

[4] Quantitative Statistical Stability for the Equilibrium States of Piecewise Partially Hyperbolic Maps. (article - Discrete and Continuous Dynamical Systems - Click here)

[3] Lipschitz regularity of the invariant measure of Random Dynamical Systems (article - Journal of Fixed Point Theory and Applications - Click here)

[2] Hölder Regularity and Exponential Decay of Correlations for a class of Piecewise Partially Hyperbolic Maps (article - Nonlinearity - Click here)

[1] Spectral Gap and quantitative statistical stability for systems with contracting fibers and Lorenz like maps (article - Discrete and Continuous Dynamical Systems - Click here)

Permanent preprints (I do not intend to publish them in journals)

The following technical material are peripheral results which are already published as attachments of other articles.

[1] On Disintegrating Measures For Skew Products

[2] Lifting Ergodic Measures

Lecture Notes (For fun...take care!)

[1] The Transfer and Perron-Frobenius Operators

[2] Spectral Gap and Statiscal Properties for Piecewise Expanding Maps

Contact Information

Profissional address: Av. Lourival Melo Mota, s/n. Tabuleiro do Martins, CEP:57072-900, Maceió - AL, Instituto de Matemática.

Email: rafael.lucena@im.ufal.br

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