godofredo iommi

Godofredo Iommi


	Facultad de Matemática, Pontificia Universidad Católica de Chile (UC).
	Av. Vicuña Mackenna 4860, Santiago, Chile.
	Phone: (56-2) 2354 44 66
	Office: 308.
	e-mail: giommi (at) mat.uc.cl

I am an associate professor at the Facultad de Matemáticas of Pontificia Universidad Católica de Chile. I am also a member of the Chilean research group on Dynamical Systems. A programme of the dynamical systems seminar of Santiago can be found here.
My main interests are Ergodic Theory, Dimension Theory and Dynamical Systems.

Papers and Preprints.

(see also Arxiv or ORCID).

Multifractal Analysis for countable Markov shifts Ergodic Theory and Dynam. Systems vol. 25 no. 6, 1881-1907 (2005).
Suspension flows over countable Markov shifts (with Luis Barreira) 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 (with Luis Barreira) Nonlinearity 21, 2211-2219 (2008).
The frequency of digits in the Lüroth expansion (with Luis Barreira) Journal of Number Theory vol. 129 no.6, 1479-1490 (2009). Corrections
The Lyapunov spectrum is not always concave (with Jan Kiwi ) 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 (with Mike Todd). Communications in Mathematical Physics 300, 65-94 (2010).
Multifractal analysis and phase transitions for hyperbolic and parabolic horseshoes (with Luis Barreira). Israel Journal of Mathematics vol.181 347--379 (2011).
Dimension theory for multimodal maps (with Mike Todd ). 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 (with Thomas Jordan) Communications in Mathematical Physics 320, 475-498 (2013).
Transience in dynamical systems (with Mike Todd). Ergodic Theory and Dynam. Systems vol 33, no 5, 1450-1476 (2013).
Thermodynamic formalism for interval maps: inducing schemes (with Mike Todd) 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 (with Thomas Jordan) Int. Math. Res. Not. IMRN 2, 460-498 (2015).
Multifractal analysis of Birkhoff averages for countable Markov maps (with Thomas Jordan) Ergodic Theory and Dynam. Systems vol. 35, no 08, 2559-2586 (2015).
Recurrence and transience for suspension flows (with Thomas Jordan and Mike Todd). Israel Journal of Mathematics vol. 209, Issue 2, 547–592 (2015).
The scaling mean and a law of large permanents (with Jairo Bochi and Mario Ponce). Advances in Mathematics 292, 374-409 (2016).
Transience and multifractal analysis (with Thomas Jordan and Mike Todd ). 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 (with Felipe Riquelme and Aníbal Velozo) Israel Journal of Mathematics 225. no 2, 609-659 (2018).
Time changes for flows and thermodynamic formalism (with Italo Cipriano). Nonlinearity 32. 2848-2874 (2019).
Hidden Gibbs measures on shift spaces over countable alphabtes (with Camilo Lacalle and Yuki Yayama). Stochastics and Dynamics 20, no 4, 2050028 (2020).
Upper semi-continuity of entropy in non-compact settings (with Mike Todd and Aníbal Velozo). Mathematical Research Letters 27. 1055-1077 (2020).
Measures of maximal entropy for suspension flows. (with Aníbal Velozo) Math. Z. 297, no 3-4, 1473-1482 (2021).
Pressure, Poincaré series and box dimension of the boundary (with Aníbal Velozo). Nonlinearity 34 no 6. 3936-3952 (2021).
The space of invariant measures for countable Markov shifts (with Anibal Velozo). Journal d'Analyse Mathematique 143 no.2 461-501 (2021).
Escape of entropy for countable Markov shifts. (with Mike Todd and Aníbal Velozo). Advances in Mathematics 405, Paper No. 108507 (2022).
Perfect Matchings in Inhomogeneous Random Bipartite Graphs in Random Enviroment. (with Jairo Bochi and Mario Ponce) CUBO 24. no 2. 263-272 (2022).
Differentiability of the pressure in non-compact spaces (with Mike Todd). Fundamenta Mathematicae 259, Vol.2 151--177 (2022).
The Halász-Székely barycenter (with Jairo Bochi and Mario Ponce). Proc. Edinburgh Math. Soc. (2) 65, no.4, 881-911 (2022).

Notes.

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 (2012).
An ergodic theorem for permanents of oblong matrices (with Jairo Bochi and Mario Ponce). (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.).
Means of digits in continued fractions (2021).

Lecture notes.

Cálculo Real. (2014) Lecture notes for the courses of calculus and analysis in one variable (in Spanish)
The Mean, The Maximal and The Pointwise Ergodic Theorems (2021).

Last modified 1 of March 2023.