- Email: Eugen.Mihailescu at imar.ro
- Mailing address: Institute of Mathematics "Simion Stoilow" of the
P. O. Box 1-764, RO 014700,
Main Research Directions:
- Professor/Principal Researcher I, Institute of Mathematics of
the Romanian Academy, since Feb 2014.
- Habilitation, Institute of Mathematics of the Romanian Academy, May
- Associate Professor/Principal Researcher II, Inst. of
Mathematics of the Romanian
- Visiting Professor,
Department of Mathematics, Texas A & M
University, USA, 1999-2001.
- Visiting Professor,
Department of Mathematics, University of North Texas, USA, 2002-Feb.
- Principal Researcher III, Inst. of Mathematics of the Romanian
Academy (Center of Excellence of EU), 1999-2006.
- Graduate Teaching Assistant and Graduate Researcher,
Department of Mathematics,
University of Michigan USA, 1995-1999.
- Research assistant, Inst. of Mathematics of the Romanian Academy,
- Dynamical Systems and Smooth Ergodic Theory.
- Dimension and Thermodynamic Formalism.
- Fractals and Probability Theory. Complex Dynamics.
Visiting Positions/Research Visits:
- Univ. Lille, France, May 2016.
- Univ of North Texas, Denton, USA, Mar 2015.
- Institut des Hautes Etudes Scientifiques (IHES), Bures-sur-Yvette,
Paris, France, 3 months, 2013-2014.
- University of Bremen, Germany, 3 months, March-May 2012.
- University of Michigan, Ann Arbor, USA, (2 weeks) Sept 2011.
- Max Planck Inst Mathematik, Bonn, Germany, May 2011.
- Erwin Schroedinger Mathematical Institute, Vienna, Austria, June
- Instituto de Matematica Pura e Aplicada (IMPA), Rio de Janeiro,
Brazil, Febr 2008.
- Univ. of North Texas, Denton, USA, Febr - March 2007.
- Goettingen University, Germany, Dec 2006.
- Univ. Paris 6, France, Oct. 2006.
- University of North Texas, USA, Oct. 2005.
- Humboldt Univ. Berlin, Germany, March - May 2005.
- Univ Pisa -Centro de Giorgi, Italy, Nov 2004.
- Univ. of North Texas, USA, Oct 2004.
- ICTP, Trieste, Italy, Jul 2004.
- IMPAN - Banach Center, Warsaw, Poland, Apr 2004.
- Inst Henri Poincare, Paris, Oct 2003.
- Scuola Normale Superiore, Pisa, Italy, Apr 2002.
Member of the Editorial Board of:
Research Grants/Conference organization/Awards:
- CNRS-IMAR grant 2015 with Univ Lille.
- Organizer "Ergodic theory and dynamics" session,
International Congress of Romanian Mathematicians, Iasi, June 2015.
- Co-organizer with B. Stratmann of the workshop "Differentiable
ergodic theory, dimension theory and stable foliations", Mathematisches
ForschungsInstitut Oberwolfach, Germany, 28 Sep-4 Oct 2014.
- Research project "Dynamical systems and smooth ergodic theory" at
IHES, Bures-sur-Yvette, France, 3 months 2013-2014.
- Frequent refereeing for many prestigious international journals.
- Project Director/Team Leader, Grant PN II-IDEI Cercetare
"Numerical invariants and geometric
properties for classes of dynamical systems" 2009-2011, from
- Annual awards from CNCSIS (Romania) for research papers published.
- CNCSIS prize for Habilitation thesis, 2015.
- Member Global Organizing Committee, 8-th
AIMS International Conference on
Dynamical Systems and Applications,
Dresden, Germany, May 2010.
- Co-organizer, with B. Stratmann
of the "Hyperbolic Dynamics and
Ergodic Theory" Section,
AIMS International Conference on
Dynamical Systems and Applications,
Dresden, Germany, May 2010.
- Prize "Simion Stoilow" of the
Romanian Academy, 2007.
- Reviewer for Zentralblatt Math, and Math Reviews.
- Participant in an NSF (National Science Foundation) Grant in Dynamics
and Ergodic Theory, Univ. North Texas (M. Urbanski), Feb.-March 2007.
- Member of the research team of grant CEEX 2006-2008, "Analiza
complexa si domenii conexe", from the Romanian Ministry of Education and
Research. Member also in other research grants in analysis, in the IMAR
- Co-organizer scientific exchange program in Dynamical Systems,
Romanian and Polish Academies,
- Rackham Research Fellowship, University of Michigan , USA, 1999.
- Teaching/Research Assistantships, Univ. of Michigan, Ann Arbor, USA,
- National Merit Fellowships, Univ. of Bucharest, 1990-1995.
Full version of my CV.
- Random countable iterated function systems with overlaps and
applications, joint with M. Urbanski, Advances in Mathematics, vol
298 (2016), 726-758.
Overlap functions for measures in conformal iterated function systems,
joint with M. Urbanski, Journal of Statistical Physics, vol. 162
(2016), no. 1, 43-62.
Measure-theoretic degrees and topological pressure for non-expanding
transformations, joint with M. Urbanski, Journal of Functional
Analysis, vol 267 (2014), no.
estimates for the
stable dimensions of fractal sets with
variable number of foldings, joint with B. Stratmann, International
Mathematics Research Notices, vol. 2014, no. 23, 6474-6496, 2014.
Equilibrium measures on saddle sets of holomorphic maps on P^2, joint
with J. E Fornaess, Mathematische Annalen, vol. 356, 1471-1491,
Measure-theoretic asymptotic degrees and non-expanding
transformations, Oberwolfach Reports , Vol. 11, 4, 2014,
2604-2609, Springer Verlag.
- Quantization coefficients in infinite systems, joint with M. Roychodury,
Kyoto Journal of
Mathematics, 55 (2015), 857-873.
production for a class of inverse SRB measures, joint with M.
Urbanski, Journal of Statistical Physics, vol. 150, no.5, 881-888,
- Hausdorff dimension of
limit sets of countable conformal iterated
function systems with overlaps, joint with M. Urbanski,
Contemporary Mathematics, vol. 600, American Mathematical Society,
- Geometric and ergodic aspects in conformal dynamics on invariant
fractals, Ann. Univ. Bucharest Math. Ser. 5 (LXIII) (2014), no. 1,
- Equilibrium measures, prehistories
distributions and fractal
dimensions for endomorphisms, Discrete and Continuous Dynamical
Systems, vol. 32, no. 7, 2485-2502, 2012. (ISI journal)
- On some coding and mixing properties on
folded fractals, Monatshefte fuer Mathematik, vol. 167, no. 2,
- Higher dimensional expanding maps and
Proceedings of the American Mathematical Society, vol.141 (2013),
- Hyperbolic dynamics on folded
saddle sets, Thermodynamic Formalism,
Geometry and Stochastics, MF Oberwolfach Reports 3/2012, 31-34,
- Approximations of Gibbs
states of arbitrary Holder potentials on hyperbolic folded sets ,
Discrete and Continuous Dynamical Systems, vol. 32, no. 3, 2012,
Inverse limits and statistical properties for chaotic implicitly
defined economic models, Journal of Mathematical Analysis and
Applications, vol. 394, no.2, 2012, 517-528. (ISI journal)
On a class of stable conditional measures, Ergodic Theory and
Dynamical Systems, vol. 31, no. 5, 1499-1515, 2011. (ISI journal)
- Unstable directions and
for a family of skew
products with overlaps in fibers, Mathematische Zeitschrift,
2011, 733-750. (ISI journal)
- Local geometry and dynamical behavior on folded basic sets,
of Statistical Physics, vol. 142, 2011, 154-167. (ISI journal)
- Hausdorff dimension of the limit
set for conformal iterated function
systems with overlaps, joint with M. Urbanski, Proceedings
of the American Mathematical Society, vol. 139, 2011, 2767-2775.
- Asymptotic distributions of
preimages for endomorphisms, Ergodic Theory and Dynamical
vol. 31, 2011, 911-935. (ISI journal)
- Relations between stable dimension and the
preimage counting function
on basic sets with overlaps, joint with M. Urbanski, Bulletin of
London Mathematical Society, vol. 42, 2010, 15-27. (ISI journal)
- Physical measures for multivalued inverse
iterates near hyperbolic repellors, Journal of Statistical
vol. 139, no. 5, 2010, 800-819 (ISI journal).
- Metric properties of some fractal sets
and applications of inverse pressure, Mathematical
Proceedings Cambridge Phil. Soc., vol. 148, no.3, May 2010, 553-572.
- Ergodic properties for some non-expanding non-reversible systems,
Nonlinear Analysis: Theory, Methods & Applications, vol. 73, 2010,
3779-3787. (ISI journal)
- Dynamics on higher dimensional real or complex fractals,
Revue Roumaine de Mathematiques Pures et Appliquees, vol. LIV,
- Metric properties and dynamics for
conformal maps, Proceedings of the International Congress of Romanian
Mathematicians Bucharest 2007, pg. 161-169, Ed. Academiei 2009.
- Transversal families of
hyperbolic skew products , joint with M.
Urbanski, Discrete and Continuous Dynamical Systems, vol. 21, no.3,
907-928, 2008. (ISI journal)
- Inverse pressure estimates and the independence
of stable dimension for non-invertible maps, joint with M. Urbanski,
of Mathematics, vol. 60, no. 3, 658-684, 2008. (ISI journal)
- Unstable manifolds and Holder
structures associated with non-invertible maps, Discrete and
Systems, 14, 2006, no 3, 419-446. (ISI journal)
- Estimates for the stable dimension for
holomorphic maps, joint with M. Urbanski, Houston Journal of
Mathematics, 31 (2), 2005, 367-389. (ISI journal)
- Inverse topological pressure with
applications to holomorphic dynamics in several variables, joint with
Mariusz Urbanski, Communications in Contemporary Mathematics,
2004, 653-682. (ISI journal)
- Holomorphic maps for which the unstable
manifolds depend on prehistories, joint with M. Urbanski,
Discrete and Continuous Dynamical Systems, vol.9, no.2, 2003. (ISI
- The set
K- for hyperbolic non-invertible maps, Ergodic Theory
and Dynamical Systems, vol. 22, June 2002, 3, 873-888. (ISI journal)
- Applications of thermodynamic formalism
in complex dynamics on P2, Discrete and Continuous
Dynamical Systems, vol. 7, 4, October 2001, 821-836. (ISI journal)
- Periodic points for actions of tori in Stein manifolds,
Mathematische Annalen 314, 1999, no 1, 39-52. (ISI journal)
- PH.D Thesis, Univ. of Michigan Press, 1999.
- A class of functions which are continuous but nowhere monotonous,
Annals of the University of Bucharest, 42/43, 1993/94, 63-71.
- On some topologies on the space of analytic coherent subsheaves,
Revista Matematica TUNTCD, 1994, Bucuresti
Brief research description
I am interested in relations between dynamics, dimension theory, ergodic
theory and fractal geometry,
smooth transformations and for iterated function systems. Some
of the areas that I worked in are: dynamics of hyperbolic endomorphisms,
dimension theory for fractals, thermodynamic formalism on
non-invertible maps, probabilities on fractals, SRB measures, chaotic
behaviour, various notions of
and pressure, finite or infinite iterated
function systems (with or without overlaps),
complex dynamics in several variables,
measures and positive currents defined
dynamically, Julia sets, attractors, quantization for IFS, etc.
I am also interested in applications of dynamics and ergodic theory to
chaos theory, number theory, economics.
- Some Selected Talks:
- Fractals and Related Fields III, Porquerolles, France, Sep 2015.
- Millican Colloquium, Univ North Texas, USA, Mar 2015.
- Differentiable Ergodic Theory, Dimension Theory and Stable
Foliations, Oberwolfach, Germany, Oct 2014.
- Logic and Dynamics, Denton, USA, June 2014.
- Fractal Geometry and Stochastics Conference, Tabarz, Germany, Mar
- IMAR Monthly Lecture, Bucharest, Feb 2014.
- Ovidius University Analysis Workshop, Constanta, Romania, May 2013.
- XI-eme Colloque Franco-Roumain de Mathematiques Appliquees, Workshop
Equations aux Derivees Partielles et Applications, Bucharest, Aug. 2012.
- Colloquium Department of Mathematics, University of Bremen,
Germany, May 2012.
- Dynamics and Geometry Seminar, University of Bremen, Germany, May
- Thermodynamical formalism, stochastics and geometry workshop,
Forschungsinstitut Oberwolfach, Germany, Jan. 2012.
- Higher dimensional dynamics seminar, University of Michigan, Ann
USA, Sept. 2011.
- Seventh Congress of Romanian Mathematicians, Brasov, July 2011.
- Hyperbolic Dynamics session, 8-th AIMS International Conference on
Differential Equations, Dresden, Germany, May 2010.
- Dynamics Conference, City University of New York, New York,
USA, June 2010.
- Dynamical Systems Session, First Pacific Rim Mathematical Association
Congress, Sydney, Australia, July 2009.
- Dynamical Systems Conference II, Denton, USA, May 2009.
- Workshop on Recent Trends in Complex Analysis and Related Topics and
the 11-th Romanian-Finnish Seminar, Alba-Iulia, Romania, August 2008.
- Dynamics Seminar, Instituto de Matematica Pura e Aplicada, Rio de
Janeiro, Brazil, February 2008.
- 6-th International Congress of Romanian Mathematicians, Bucharest,
- Dynamical Systems Seminar, Denton, USA, March 2007
- Conformal Structures Workshop, Inst. fuer Mathematische Stochastik,
Univ. Gottingen, Germany, Dec. 2006
- Dynamical Systems and Harmonic Analysis Seminar, Univ.
Paris 11, Orsay, France, Oct. 2006
- Dynamical Systems Seminar, Univ. North Texas, USA, Oct. 2005
- International Conference on Complex Analysis and Related Topics and
the Romanian-Finnish Seminar, Cluj, Romania, Aug. 2005
- Holomorphic Dynamics Seminar, Centro de Giorgi, Univ. Pisa,
Italy, Nov. 2004
- Millican Colloquium, Univ. North Texas, USA, Oct. 2004
- Dynamical Systems Seminar, Univ. of Warsaw, Poland, May 2004
- Complex Analysis and Dynamics Seminar, IMPAN-Banach Center, Warsaw,
- International Conference on Dynamical Systems, Denton, USA, May 2003
- Conference on Holomorphic Dynamics in Several Variables, Scuola
Pisa, Italy,Apr 1999
- Complex Analysis Seminar, Texas A&M Univ., USA, April 1999
- Midwest Several Complex Variables Conference, Bloomington, USA, Feb.
- Complex Dynamics Seminar, Univ. Michigan, USA, Nov. 1998
Advising and Teaching
Students interested in pursuing a degree (Doctorate
Master), in dynamical systems, probability on fractals, or ergodic
welcome to contact me.
In Fall 2015 I teach a graduate course on "Invariant probabilities and
applications", at SNSB Bucharest. In
Spring 2014 I taught a graduate course on "Differentiable Ergodic Theory"
at SNSB-Normal Superior School of Bucharest.
During the academic year 2009-2010 I taught a Masters course on
"Analysis on fractals" at SNSB-Normal Superior School of Bucharest.
Students at SNSB that are interested in dynamical systems, ergodic theory,
measure theory or complex analysis/dynamics can contact me at the email
address above, for further
study and/or problems in these areas.
In 2008-2009 I taught a Masters course on "Differentiable Dynamics" at
SNSB (Normal Superior School of Bucharest).
In 2007-2008 I taught a Masters course on "Topology and dynamics for
hyperbolic maps" at SNSB.
In 2006 I taught two advanced courses at SNSB, for some selected best
students of Romanian universities.
The first course was "Introduction to dynamical systems" (Spring 2006),
and the second is a Masters course "Ergodic theory with applications to
dynamics" (Fall 2006).
At SNSB I directed several theses of students, and have been also on
several PH.D Thesis Committees at IMAR.
My teaching experience consists also in the diverse courses I
taught in the
mathematics departments of the University of Michigan, University of
North Texas, Texas A & M University, Universitatea Politehnica Bucuresti,
University of South Carolina, etc.
I taught various courses and seminars, like Probability
(Univ. of North Texas 2002), Calculus 115 (Univ.
of Michigan 1995-1997), Calculus II-- Math 215 with Maple (Univ.of
Michigan 1998-1999), Differential Equations III (Texas A& M Univ.
2000-2001), Real Analysis, and Advanced Mathematics (Univ. Politehnica
Bucuresti, 2001-2002), Business
Calculus (Univ. North Texas 2002), etc.
I participated in the elaboration of teaching curriculae and
exam problems and the training of teaching assistants at Univ. of
Michigan, Texas A& M Univ. and Univ. of North Texas.
During my Visiting Professorship at Texas A& M
University, I supervised three teaching
assistants and two grading assistants for my Calculus and Differential
Equations courses. At Univ. of North Texas I also
supervised a grading assistant.
Created initially August 2000.