Facultad de Matemática, Pontificia Universidad Católica de Chile (PUC).
Av. Vicuña Mackenna 4860, Santiago, Chile.
Phone: (56-2) 2354 44 66
Fax: (56-2) 25525916.
e-mail: giommi (at) mat.puc.cl
I am an associate professor at the
Facultad de Matemáticas
Pontificia Universidad Católica de Chile
. I am also a member of the Chilean research group on
and of the project
New Trends in Ergodic Theory
. A programme of the dynamical systems seminar of Santiago can be found
My main interests are Ergodic Theory, Dimension Theory and Dynamical Systems.
Papers and Preprints.
Multifractal Analysis for countable Markov shifts
Ergodic Theory and Dynam. Systems vol. 25 no. 6, 1881-1907 (2005).
Suspension flows over countable Markov shifts
) Journal of Statistical Physics vol.124 no.1, 207-230 (2006).
Multifractal Analysis for the Exponential family
(with B. Skorulski) Discrete and Continuous Dynamical Systems vol.16 no.4, 857-869 (2006).
Ergodic Optimization for Renewal type shifts
Monatshefte fur Mathematik vol.150 no.2, 91-95 (2007).
Partial quotients of continued fractions and beta-shifts
) Nonlinearity 21, 2211-2219 (2008).
The frequency of digits in the Lüroth expansion
) Journal of Number Theory vol. 129 no.6, 1479-1490 (2009).
The Lyapunov spectrum is not always concave
) Journal of Statistical Physics vol.135 no.3, 535-546 (2009).
Multifractal analysis of Lyapunov exponent for the backward continued fraction map.
Ergodic Theory and Dynam. Systems vol. 30 no.1 211-232 (2010).
Natural equilibrium states for multimodal maps
). Communications in Mathematical Physics 300, 65-94 (2010).
Multifractal analysis and phase transitions for hyperbolic and parabolic horseshoes
). Israel Journal of Mathematics vol.181 347--379 (2011).
Dimension theory for multimodal maps
). Annales Henri Poincaré 12, 591-620 (2011).
Almost-additive thermodynamic formalism for countable Markov shifts
(with Yuki Yayama). Nonlinearity 25, 165-191 (2012).
The Lyapunov spectrum as the Newton method
. Physica A, 391, vol.9 2848-2852 (2012).
Phase transitions for suspension flows
) Communications in Mathematical Physics 320, 475-498 (2013).
Transience in dynamical systems
). Ergodic Theory and Dynam. Systems vol 33, no 5, 1450-1476 (2013).
Thermodynamic formalism for interval maps: inducing schemes
) Dyn. Sys. Issue edited by Quas and Vaienti. vol. 28 Issue 3, 354-380 (2013).
Zero temperature limits of Gibbs states for almost-additive potentials
(with Yuki Yayama) Journal of Statistical Physics 155, 23-46 (2014).
Multifractal analysis of quotients of Birkhoff sums for countable Markov maps
) Int. Math. Res. Not. IMRN 2, 460-498 (2015).
Multifractal analysis of Birkhoff averages for countable Markov maps
) Ergodic Theory and Dynam. Systems vol. 35, no 08, 2559-2586 (2015).
Recurrence and transience for suspension flows
). Israel Journal of Mathematics vol. 209, Issue 2, 547–592 (2015).
The scaling mean and a law of large permanents
). Advances in Mathematics 292, 374-409 (2016).
Transience and multifractal analysis
) Annales de l'Institut Henri Poincare / Analyse non lineaire 34. no 2, 407-421 (2017).
Weak Gibbs measures as Gibbs measures for asymptotically additive sequences
(with Yuki Yayama) Proceedings of the AMS 145, no 4. 1599-1614 (2017).
Entropy in the cusp and phase transitions for geodesic flows
and Aníbal Velozo) Israel Journal of Mathematics 225. no 2, 609-659 (2018).
Time changes for flows and thermodynamic formalism
Pressure, Poincaré series and box dimension of the boundary
(with Aníbal Velozo).
Hidden Gibbs measures on shift spaces over countable alphabtes
(with Camilo Lacalle and Yuki Yayama).
Upper semi-continuity of entropy in non-compact settings
). To appear in Mathematical Research Letters.
The space of invariant measures for countable Markov shifts
The Bowen Formula: Dimension Theory and Thermodynamic Formalism
Notes from VII Escuela de Sistemas Dinámicos, Valparaíso, 2008.
The dimension theory of number theoretically defined sets
Notes from Encuentro SOMACHI 2008, Valparaíso, 2008.
Funciones continuas con máximos locales densos
Revista del Jóven Matemático no.3, 27-34 (2012) (in Spanish).
Thermodynamic formalism for the positive geodesic flow on the modular surface
. (Superceded by "Phase transitions for suspension flows"by Iommi and Jordan).
The Besicovitch formula
An ergodic theorem for permanents of oblong matrices
). (2015) (After the completion of this paper, we were informed that Theorem 1 is a particular case of Theorem U in J. Aaronson, R. Burton, H. Dehling, D. Gilat, T. Hill, B. Weiss. "Strong laws for L– and U–statistics." Trans. Amer. Math. Soc. 348 (1996), no. 7, 2845–2866.).
Perfect Matchings in random bipartite graphs in random environment
The following are lecture notes for the courses of calculus and analysis in one variable (in Spanish).
Last modified 1st of March of 2019.