- 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:
- Principal Researcher II/Associate Professor, Inst. of
Mathematics of the Romanian
Academy, since Febr. 2006.
- Visiting Professor,
Department of Mathematics, Texas A & M
- Visiting Professor,
Department of Mathematics, University of North Texas, 2002-Feb. 2003.
- 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,
Research Appointments and Visits:
- Dynamical Systems; Hyperbolic Endomorphisms and Dimension
- Smooth Ergodic Theory; Thermodynamical Formalism; Fractals.
- Complex Dynamics; Complex Analysis.
- Applications to Chaos Theory, Statistical Physics, etc.
Member of the Editorial Board of:
- University of Bremen, Germany, 3 months, March-May 2012.
- University of Michigan, USA, (2 weeks) Sept. 2011.
- Erwin Schrodinger Mathematical Institute, Vienna, Austria, June 2008.
- 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. of North Texas, USA, Sep.-Oct. 2004.
- IMPAN - Banach Center, Warsaw, Poland, Apr. 2004.
- Univ. Pisa - Centro de Giorgi, Italy, Apr. 2002 and Nov. 2004.
- Project Director/Team Leader, Grant PN II-IDEI Cercetare
"Numerical invariants and geometric
properties for classes of dynamical systems" 2009-2011, from
- Member of the Global Organizing Committee, 8-th
AIMS International Conference on
Dynamical Systems and Applications,
Dresden, Germany, May 2010.
- Co-organizer, with Bernd Stratmann
of the "Hyperbolic Dynamics and
Ergodic Theory" Section,
AIMS International Conference on
Dynamical Systems and Applications,
Dresden, Germany, May 2010.
- CNCS (Romania) prizes for papers published in 2011.
- CNCSIS (Romania) prizes for papers published in 2010.
- CNCSIS Prize for papers published in 2008.
- Prize "Simion Stoilow" of the
Romanian Academy, 2007.
- 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 and participant in the Scientific Exchange Program
Romanian and Polish Academies, "Holomorphic Dynamics and Ergodic Theory",
- Frequent refereeing for many prestigious international journals.
- Rackham Research Fellowship, University of Michigan , USA, 1999.
- National Merit Fellowships, Univ. of Bucharest, 1990-1995.
- Reviewer for Zentralblatt Math. and Math. Reviews.
Full version of my CV.
- Equilibrium measures on saddle sets of holomorphic maps on P^2, joint
with J. E Fornaess, Mathematische Annalen, Online First 2013.
production for a class of inverse SRB measures, joint with M.
Urbanski, Journal of Statistical Physics, Online First 2012.
- Upper estimates for the stable dimensions of fractal sets with
variable number of foldings, joint with B. Stratmann, preprint 2012.
- Hausdorff dimension of limit sets of countable conformal iterated
function systems with overlaps, joint with M. Urbanski, to appear
Contemporary Mathematics, AMS, 2013.
- 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
toral extensions, to appear
Proceedings of the American Mathematical Society, 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)
- Local geometry and dynamical behavior on folded basic sets,
of Statistical Physics, vol. 142, 2011, 154-167. (ISI journal)
- Unstable directions and
for a family of skew
products with overlaps in fibers, Mathematische Zeitschrift,
2011, 733-750. (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)
- 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.
- 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)
- 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, 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
I am interested in the relations between Dimension Theory and
Thermodynamic Formalism with the Dynamics of
Smooth Transformations, especially in the case of
endomorphisms. I am also interested in Chaos Theory, Ergodic Theory and
Dynamics on Fractals (saddle basic sets, hyperbolicity, chaotic behavior,
complex dynamics in one or several variables, Lyapunov exponents,
measures, iterated function systems, hyperbolic flows, attractors, etc.).
Currently I am interested in a relatively recent field, that of applications
theory and thermodynamical
formalism to the dynamics of higher dimensional dynamical systems.
In one variable, complex dynamics was born when Fatou and Julia studied,
at the begining of the XX-th
century, normal families of holomorphic functions and what are now
called the Fatou components and Julia
Given the essential geometric differences that appear when one considers several complex variables it is
justified to expect new and interesting phenomena occuring in this case.
My thesis studied actions of tori on Stein manifolds and consequences on
the dynamics of periodic
points, and on the other hand, the "opposite" case of strongly hyperbolic endomorphisms.
One can remark that among examples of Stein manifolds with actions of circles we find the Fatou
components of a holomorphic endomorphism in a projective complex space.
At the moment I am working on applications of thermodynamic formalism in
higher dimensional conformal dynamics of non-invertible maps. Notions from
thermodynamics have found
recently powerful applications also to complex dynamics,
especially regarding questions about Hausdorff dimension of invariant sets and equilibrium measures.
Here also hyperbolicity plays a very important role.
I have studied the case of Axiom A non-invertible maps on projective
spaces and their stable dimension. Here generalizations of the usual
notions of topological entropy and pressure are in order, which will
take into consideration the prehistories of points.
The dynamics of hyperbolic non-invertible maps is different than the
diffeomorphisms, although there are some common trends.
In this case, the unstable tangent spaces (and hence also the unstable
manifolds) depend on entire prehistories; therefore the unstable manifolds
do not form a nice (Lipschitz) lamination near the basic set and the
stable dimension cannot be written in general as the solution of a Bowen
equation involving the usual (forward) pressure.
Still, for conformal maps, the stable dimension is equal in many
cases to the zero of the inverse pressure. The notion of inverse
pressure (introduced by me and M. Urbanski) is better suited to deal
with some aspects of non-invertible maps, than the classical topological
pressure. The dimension theory for such maps is very rich and beautiful,
and has connections with many fields.
This direction involves the study of equilibrium and conformal measures,
attractors/repellors/saddle basic sets, transfer operators, examples from
one or higher dimensional complex dynamics, and symbolic dynamics.
- Some Invited Talks:
- 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, May 2012.
- Thermodynamical formalism, stochastics and geometry workshop,
Forschungsinstitut Oberwolfach, Germany, Jan. 2012.
- Higher dimensional complex dynamics seminar, University of Michigan,
USA, Sept. 2011.
- Seventh Congress of Romanian Mathematicians, Brasov, July 2011.
- Special session, 8-th AIMS International Conference on Dynamical
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, April 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
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.
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.
Most of them were classical proof courses; a few others were following
the Harvard Calculus Reform of emphasizing
real life applications of mathematics and the involvement of
computers in the teaching process (Mathlab, Maple, etc.)
During my two-year Visiting Professorship at Texas A& M
University, I supervised three teaching
assistants and two grading assistants for the Calculus and Differential
Equations courses that I taught. At Univ. of North Texas I also
supervised a grading assistant.
Created initially August 2000.