Konstantin Athanassopoulos

Professor

Department of Mathematics and Applied Mathematics
University of Crete
University Campus
GR-700 13 Voutes, Iraklion, Crete
GREECE

Office: Gamma 320
Tel: (0030)-2810-393825 (office) FAX: (0030)-2810-393881
Home Address: Nteli Drakou 21, GR-714 09 Iraklion, Crete, GREECE

E-mail: athanako@uoc.gr

My CV in english (ps, pdf) and in greek (ps, pdf) . A description of my research in greek (ps, pdf) .

Research Interests
Dynamical Systems
Differential Geometry and Topology
Ergodic Theory

Research Publications
  1. D+ stable dynamical systems on 2-manifolds, Math. Z. 196 (1987), 453-462. (pdf)
  2. (with P. Strantzalos) On minimal sets in 2-manifolds, J. reine angew. Math. 388 (1988), 206-211. (pdf)
  3. The flow near nontrivial minimal sets on 2-manifolds, Math. Proc. Camb. Phil. Soc. 108 (1990), 569-573. (pdf)
  4. Cohomology and asymptotic stability of 1-dimensional continua, Manuscripta Math. 72 (1991), 415-423. (pdf)
  5. A characterization of Denjoy flows, Bull. London Math. Soc. 24 (1992), 83-86. (pdf)
  6. Some aspects of the theory of asymptotic cycles, Expositiones Math. 13 (1995), 321-336. (pdf)
  7. (with A. Manoussos) Minimal flows on multipunctured surfaces of infinite type, Bull. London Math. Soc. 27 (1995), 595-598. (pdf)
  8. One-dimensional chain recurrent sets of flows in the 2-sphere, Math. Z. 223 (1996), 643-649. (pdf)
  9. Flows with cyclic winding numbers groups, J. reine angew. Math. 481 (1996), 207-215. (pdf)
  10. (with Th. Petrescou and P. Strantzalos) A class of flows on 2-manifolds with simple recurrence, Comment. Math. Helvetici 72 (1997), 618-635. (pdf)
  11. Rotation numbers and isometries, Geom. Dedicata 72 (1998), 1-13. (pdf)
  12. Volume preserving flows with cyclic winding numbers groups and without periodic orbits on 3-manifolds, Manuscripta Math. 97 (1998), 37-44. (pdf)
  13. Periodicity criteria of Poincare-Bendixson type, Univ. Iagel. Acta Math. 36 (1998), 181-182. (pdf)
  14. Rotation of orbits and isometries, Proceedings of the 3d Panhellenic Conference of Geometry, (1999), 67-71.
  15. (with A. Alexellis) Chain recurrence in flows on the Klein bottle, Math. Proc. Camb. Phil. Soc. 127 (1999), 83-91. (pdf)
  16. Cohomology of surface minimal sets, Expositiones Math. 17 (1999), 371-374. (pdf)
  17. On the Ruelle rotation for torus diffeomorphisms, Math. Z. 234 (2000), 225-239. (pdf)
  18. Explosions near isolated unstable attractors, Pacific J. Math. 210 (2003), 201-214. (pdf)
  19. Remarks on the region of attraction of an isolated invariant set, Colloq. Math. 104 (2006), 157-167. (pdf)
  20. Pointwise recurrent homeomorphisms with stable fixed points, Topology Appl. 153 (2006), 1192-1201. (pdf)
  21. Divergence of C1 vector fields and nontrivial minimal sets on 2-manifolds, J. Differential Equations 243 (2007), 24-35. (pdf)
  22. Asymptotically stable one-dimensional compact minimal sets, Topol. Methods Nonlinear Anal. 30 (2007), 397-406. (pdf)
  23. (with C. Panagiotakis and G. Tziritas) The equipartition of curves, Computational Geom. 42 (2009), 677-689. (pdf)
  24. The Ruelle rotation of Killing vector fields, Colloq. Math. 116 (2009), 243-247. (pdf)
  25. Denjoy C1 diffeomorphisms of the circle and McDuff's question, Expositiones Math. 33 (2015), 48-66. (pdf)
  26. Coherent measures and the unstable manifold of isolated unstable attractors, Dynamical Systems 34 (2019), 434-442. (pdf)
  27. A sufficient condition for the logarithm of the derivative of a Denjoy C1 diffeomorphism to be a measurable coboundary, preprint. (pdf)
  28. On the existence of absolutely continuous conformal measures, preprint. (pdf)

Teaching in the academic year 2024-2025
Winter semester: (i) Topology ( Lecture Notes and Exercises ), (ii) Introduction to Riemannian Geometry , graduate course ( Lecture Notes ).
Office hours in the winter semester 2024-2025: Wednesday 11:00 - 13:00 or by appointment.
Spring semester: (i) Geometry ( Lecture Notes ), (ii) Algebraic Topology-Homotopy Theory , graduate course.

Master's Thesis
Some subjects for a Master's Thesis can be found here .
Completed Master's Thesis:
  1. J. Platis, On the Godbillon-Vey invariant: Continuous variation and leaf dynamics, 1994.
  2. E. Menioudaki, Dynamical systems without periodic orbits: Counterexamples to Seifert's conjecture , 2000.
  3. J. Tsekouras, Topological characterization of conformal automorphisms of the 2-sphere: A contemporary approach , 2002.
  4. Ch. Bougas, Blaschke's conjecture and wiedersehen manifolds , 2014.
  5. B. Aimoniotis, Topological Complexity , 2014.

Seminars
The Geometry Seminar 2001-2002 at the Univ. of Crete.
The Dynamical Systems and the Geometry Seminar 2002-2003 at the Univ. of Crete.
The Geometry Seminar 2003-2004 at the Univ. of Crete.
The Dynamical Systems Seminar 2004-2005 at the Univ. of Crete.
The Dynamical Systems Seminar 2005-2006 at the Univ. of Crete.
The Geometry Seminar 2006-2007 at the Univ. of Crete.
The Dynamical Systems and the Geometry Seminar 2007-2008 at the Univ. of Crete.
The Mechanics and Symplectic Geometry Seminar 2013-2014 at the Univ. of Crete.

Lecture Notes
Course notes on Euclidean and Non-Euclidean Geometry (in Greek).
Handwritten lecture notes on elementary Topology (in Greek).
Handwritten lecture notes on Calculus III (Differential Equations) (in Greek).
Handwritten lecture notes on Functions of several variables (in Greek).
Lecture notes of the undergraduate course Differential Geometry of curves and surfaces (in Greek).
Exercises of the undergraduate course Analysis I (in Greek).
Lectures on some Classical theorems of topology in dimension 2 (in Greek).
Exercises on Differentiable Manifolds and Riemannian Geometry (in Greek).
Lectures on Poincare-Bendixson Theory given in the Summer School on Mathematics, 2002, held at Iraklion (in Greek).
A lecture on Rotation Numbers in Dynamical Systems (in Greek).
A lecture on the (Non-)Existence of periodic orbits in dynamical systems (in English).
Lecture Notes on measurable coboundaries (in English).
A lecture on The gradient structure of flows (in Greek).
A lecture on Stable and unstable minimal attractors (in English).
Six chapters of introductory Notes on Ergodic Theory of Dynamical Systems from a geometric point of view (in English).
Five chapters of introductory Notes on Symplectic Geometry (in English).
Course Notes: An introduction to smooth manifolds, deRham cohomology and characteristic classes (in English).
Course Notes: An introduction to Riemannian Geometry (in English).
Notes on Sub-Riemannian Geodesics and Volume (in English).
An introductory course in Discrete Dynamical Systems (in Greek).

Some old high school books of the greek education system
An Algebra and introductory Analysis book.
Volume A and Volume B of a book on Geometry.
A book on Euclidean Geometry .

K. Athanassopoulos, 24.01.2014