Eugen Mihailescu


Institute of Mathematics of the Romanian Academy

Professor / Principal Researcher I



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Education

Academic Employment

Research

  • Main Research Directions:
  • Visiting Positions/Research Appointments:
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  • Research Grants/Conference organization/Awards:

    Publications

    1. Random countable iterated function systems with overlaps and applications, joint with M. Urbanski, preprint 2015.
    2. Measure-theoretic degrees and topological pressure for non-expanding transformations, joint with M. Urbanski, Journal of Functional Analysis, vol 267 (2014), no. 8, 2823-2845.
    3. Upper 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.
    4. Equilibrium measures on saddle sets of holomorphic maps on P^2, joint with J. E Fornaess, Mathematische Annalen, vol. 356, 1471-1491, 2013.
    5. Measure-theoretic asymptotic degrees and non-expanding transformations, Oberwolfach Reports , Vol. 11, 4, 2014, 2604-2609, Springer Verlag.
    6. Entropy production for a class of inverse SRB measures, joint with M. Urbanski, Journal of Statistical Physics, vol. 150, no.5, 881-888, 2013.
    7. Hausdorff dimension of limit sets of countable conformal iterated function systems with overlaps, joint with M. Urbanski, Contemporary Mathematics, vol. 600, American Mathematical Society, 273-290, 2013.
    8. Geometric and ergodic aspects in conformal dynamics on invariant fractals, Ann. Univ. Bucharest Math. Ser. 5 (LXIII) (2014), no. 1, 157-168.
    9. Equilibrium measures, prehistories distributions and fractal dimensions for endomorphisms, Discrete and Continuous Dynamical Systems, vol. 32, no. 7, 2485-2502, 2012. (ISI journal)
    10. On some coding and mixing properties on folded fractals, Monatshefte fuer Mathematik, vol. 167, no. 2, 241-255, 2012, (ISI journal)
    11. Higher dimensional expanding maps and toral extensions, Proceedings of the American Mathematical Society, vol.141 (2013), 3467-3475.
    12. Hyperbolic dynamics on folded saddle sets, Thermodynamic Formalism, Geometry and Stochastics, MF Oberwolfach Reports 3/2012, 31-34, DOI: 10.4171/OWR/2012/03.
    13. Approximations of Gibbs states of arbitrary Holder potentials on hyperbolic folded sets , Discrete and Continuous Dynamical Systems, vol. 32, no. 3, 2012, 961-975. (ISI journal)
    14. 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)
    15. On a class of stable conditional measures, Ergodic Theory and Dynamical Systems, vol. 31, no. 5, 1499-1515, 2011. (ISI journal)
    16. Unstable directions and fractal dimensions for a family of skew products with overlaps in fibers, Mathematische Zeitschrift, vol. 269, 2011, 733-750. (ISI journal)
    17. Local geometry and dynamical behavior on folded basic sets, Journal of Statistical Physics, vol. 142, 2011, 154-167. (ISI journal)
    18. 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. (ISI journal)
    19. Asymptotic distributions of preimages for endomorphisms, Ergodic Theory and Dynamical Systems, vol. 31, 2011, 911-935. (ISI journal)
    20. Relations between stable dimension and the preimage counting function on basic sets with overlaps, joint with M. Urbanski, Bulletin of the London Mathematical Society, vol. 42, 2010, 15-27. (ISI journal)
    21. Physical measures for multivalued inverse iterates near hyperbolic repellors, Journal of Statistical Physics, vol. 139, no. 5, 2010, 800-819 (ISI journal).
    22. Metric properties of some fractal sets and applications of inverse pressure, Mathematical Proceedings Cambridge Phil. Soc., vol. 148, no.3, May 2010, 553-572. (ISI journal)
    23. Ergodic properties for some non-expanding non-reversible systems, Nonlinear Analysis: Theory, Methods & Applications, vol. 73, 2010, 3779-3787. (ISI journal)
    24. Dynamics on higher dimensional real or complex fractals, Revue Roumaine de Mathematiques Pures et Appliquees, vol. LIV, no.5-6, 2009, 513-524.
    25. Metric properties and dynamics for conformal maps, Proceedings of the International Congress of Romanian Mathematicians Bucharest 2007, pg. 161-169, Ed. Academiei 2009.
    26. Transversal families of hyperbolic skew products , joint with M. Urbanski, Discrete and Continuous Dynamical Systems, vol. 21, no.3, 907-928, 2008. (ISI journal)
    27. Inverse pressure estimates and the independence of stable dimension for non-invertible maps, joint with M. Urbanski, Canadian Journal of Mathematics, vol. 60, no. 3, 658-684, 2008. (ISI journal)
    28. Unstable manifolds and Holder structures associated with non-invertible maps, Discrete and Continuous Dynamical Systems, 14, 2006, no 3, 419-446. (ISI journal)
    29. Estimates for the stable dimension for holomorphic maps, joint with M. Urbanski, Houston Journal of Mathematics, 31 (2), 2005, 367-389. (ISI journal)
    30. Inverse topological pressure with applications to holomorphic dynamics in several variables, joint with Mariusz Urbanski, Communications in Contemporary Mathematics, vol.6, no.4, 2004, 653-682. (ISI journal)
    31. 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 journal)
    32. The set K- for hyperbolic non-invertible maps, Ergodic Theory and Dynamical Systems, vol. 22, June 2002, 3, 873-888. (ISI journal)
    33. Applications of thermodynamic formalism in complex dynamics on P2, Discrete and Continuous Dynamical Systems, vol. 7, 4, October 2001, 821-836. (ISI journal)
    34. Periodic points for actions of tori in Stein manifolds, Mathematische Annalen 314, 1999, no 1, 39-52. (ISI journal)
    35. PH.D Thesis, Univ. of Michigan Press, 1999.
    36. A class of functions which are continuous but nowhere monotonous, Annals of the University of Bucharest, 42/43, 1993/94, 63-71.
    37. On some topologies on the space of analytic coherent subsheaves, Revista Matematica TUNTCD, 1994, Bucuresti

    Curriculum Vitae

    Full version of my CV.

    Brief research description
    I am interested in relations between dynamics, dimension theory, ergodic theory and fractal geometry, for 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 saddle sets for non-invertible maps, probabilities on fractals, SRB measures, chaotic behaviour, various notions of entropy 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.

    Advising and Teaching

    Students interested in pursuing a degree (Doctorate or Master), in dynamical systems, probability on fractals, or ergodic theory are 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.

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    Created initially August 2000.