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

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

Here, you can explore what's relevant for potential international users and 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, please don't 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

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

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

[3] Lipschitz regularity of the invariant measure and statistical properties for a class of random dynamical systems (preprint - work in progress)

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

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

Preprints (do not intend to publish them.)

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

...

Oh I know it's not much but it's the best I can do

My gift is my song

And this one's for you

And you can tell everybody this is your song

It may be quite simple but now that it's done

I hope you don't mind

That I put down in words

How wonderful life is while you're in the world

...

Your Song,

Elton John, 1970