CURRICULUM VITAE FAMILY NAME: Igor FIRST NAME: Vlasenko DEGREE: Ph.D. in Mathematics (2002) BIRTHDATE: April 18, 1975 CITIZENSHIP: Ukrainian ADDRESS: Institute of Mathematics of the National Academy of Sciences of Ukraine, 3 Tereshchenkivska Street, 01601 Kyiv-4, UKRAINE Phone: +38 044 5407565 Fax: +38 044 2352010 Electronic Mail: vlasenko@imath.kiev.ua LANGUAGES: Russian (native speaker) Ukrainian (native speaker) English (good) EDUCATION a) Undergraduate and graduate studies Institution: Kiev State University, Faculty of Mathematics and Mechanics, (1992--1997) Degree: Master of Sciences in Mathematics (1997) Field of Study: Mathematics Thesis: "Topological structure of Morse-Smale diffeomorphisms" (Diploma with Honor) Thesis advisor: Prof. V. Sharko b) Postgraduate study Institution: Institute of Mathematics of the National Academy of Sciences of Ukraine, Department of Topology (1997--2001) Degree: Ph.D. in Mathematics (2002) Field of Research: geometric theory of dynamical systems Thesis: "Morse-Smale dynamical systems with discrete time on surfaces" Supervisor: Prof. V. Sharko ACADEMIC HONORS Postgraduate Studentship, Institute of Mathematics of the National Academy of Sciences of Ukraine (1997--2001) M.Sc.--Diploma with Honor, Kiev State University (1997) Additional stipend for excellent students, Kiev State University (1992--1997) Stipend of National Academy of Science of Ukraine (2002--2004) President of Ukraine Prize for Junior Scientists (2003) RESEARCH POSITIONS 2001 to 2002 Junior Research Associate at the Department of Topology of Institute of Mathematics of the National Academy of Sciences of Ukraine. 2002 to 2005 Research Associate at the Department of Topology of Institute of Mathematics of the National Academy of Sciences of Ukraine. 2006 to present Advanced Research Associate at the Department of Topology of Institute of Mathematics of the National Academy of Sciences of Ukraine. PRINCIPAL RESULTS (1997--2002) It is proved that the complete topological invariant of Morse-Smale dynamical systems on 2-manifolds is finite. The necessary and sufficient conditions for the topological conjugacy of Morse-Smale dynamical systems on 2-manifolds are obtained. PRINCIPAL RESULTS (2003--2008) Topological classification of regular wandering set's periodic components in cases of A-diffeomorphisms and structurally stable diffeomorphisms. Topological description of roots and commutants of Morse-Smale diffeomorphisms on surfaces. Studies of the iteration stability of invariant sets in Topological Dynamics. Found examples of iteration unstable wandering set and Birkhoff senter, an example of nonwandering set without recurrent and limit points. PRINCIPAL RESULTS (2008--2023) Development of Topological Dynamics for Trokhimchuk inner mappings (published as a book) mostly on 2-dimentional manifolds and open topological graphs. Classification of inner mappings of a circle. Numerous new topological invariants of the wandering set of inner mappings. Constructed examples of abundance of topological conjugacy classes for wandering sets of inner mappings, topological invariants of inner mappings related to holomorphic maps, an example of neutrally nonwandering points for the inner mappings that are not neutrally recurrent. Results on classification and topological conjugacy of different classes of two-dimensional inner mappings. SCIENTIFIC INTERESTS Smooth Topology, Topology of Dynamical Systems and Qualitative Theory of Dynamical Systems. Hyperbolic Dynamics and Inner Mappings Dynamics on Low-dimentional manifolds. The current topic is Topological Dynamics of Inner Mappings. PUBLICATIONS a) Books 1. Vlasenko I., Maksimenko S., Polulyah E. Topological methods in studying of groups of mappings of manifolds. //Mathematics and its applications. Proceedings of Inst. of Math. Vol. 61. Kiev. 2006. -363p. (In Russian). 2. Vlasenko I. Inner mappings and their applications. // //Mathematics and its applications. Proceedings of Inst. of Math. Vol. 101. Kiev. 2014. -225p. (In Russian). b) Referred journal publications 1.Igor Vlasenko, On the complete invariant of Morse-Smale diffeomorphisms on 2-manifolds. Part I. // Proceedings of Inst. of Math. Vol. 25. Kiev. 1998. -P. 60-85. (In Russian) 2.Igor Vlasenko, On the complete invariant of Morse-Smale diffeomorphisms on 2-manifolds. Part II. // Proceedings of Inst. of Math. Vol. 25. Kiev. 1998. -P. 86-93. (In Russian) 3.Igor Vlasenko, On relations on the set of heteroclinic points of Morse-Smale diffeomorphisms on 2-manifolds. // Methods of Functional Analysis and Topology. Vol. 5, No. 3, 1999. pp. 90-96. 4.Igor Vlasenko, On the complete invariant of Morse-Smale diffeomorphisms on unoriented surfices. // Uspekhi Mat. Nauk, v. 54, No. 5 (329), 1999. pp. 155-156 (In Russian). 5.Igor Vlasenko, Numeric characteristics on tne set of geteroclinic points of Morse-Smale diffeomorphisms on surfaces. // Ukrainian Math. Journal, v. 52, No. 10, 2000. pp. 1412-1417 6.Igor Vlasenko, Topological properties of periodic components of A-diffeomorphisms. // Ukrainian Math. Journal, v. 54, No. 8, 2002. pp. 1131-1141. (In Russian) 7.Igor Vlasenko, Topological properties of periodic components of structurally stable diffeomorphisms. // Ukrainian Math. Journal, v. 54, No. 9, 2002. pp. 1190-1199. (In Russian) 8.Igor Vlasenko, An example of 2-dimentional attractor in 4-mainfold based on expanding maps of tori. // Topology and geometry: Proceedings of UMK-2001. --Kiev: Inst. of Math., 2003. pp. 50-53. 9. I. Vlasenko, An example of irreversible Williams' solenoid. // Matematychni Studii, v. 21, No. 1, 2004. pp. 105-108. 10. I. Vlasenko, S.Maksimenko. Roots from homeomorphisms and diffeomorphisms of manifolds. // -- Kiev, 2004. -- 64 p. -- (Preprint /NAN of Ukraine. Inst. Of mathematics; 2004.8) 11. I. Vlasenko. On the iteration stability of wandering set. // Visnyk of Kiev University -- Mathematics. Mechanics. 2005. No. 14. - P. 67. 12. E.~Polulyakh, I.~Vlasenko. On iteration stability of the Birkhoff center against the power 2. // U. M. G., 2006, vol. 58, No. 5. pp. 705-707. 13. E.~Polulyakh, I.~Vlasenko. An example of nonwandering set without recurrent and limit points. // Proceedings of Inst. of Math. Vol. 3, No. 3. Kiev. 2006. pp. 45-106. (In Russian). 14. I. Yu. Vlasenko. On the dynamics of the infinite-to-one Trokhimchuk inner epimorphisms. // Proceedings of International Conference “Geometry in Odessa -- 2008”. Kiev. 2008. pp. 373-389. (In Russian) 15. I. Yu. Vlasenko. Factor-homeomorphism of Inner Epimorphism. // Proceedings of Ukrainian Math Congress - 2009. Section 2. Topology and Geometry. Kyiv, 2011. pp. 29-37. 16. I. Yu. Vlasenko. Dynamics of inner maps. // Nonlinear Oscillations. V.14 No. 2 2011 pp. 181-186 17. I. Yu. Vlasenko. Classification of the Regular Components of Two-Dimensional Inner Maps // Ukrainian Mathematical Journal vol. 66, pp. 42–49 (2014) 18. Igor Yu. Vlasenko. Abundance of topological conjugacy classes for wandering sets of inner mappings. // Proc. Intern. Geom. Center 2014 7(3). pp. 21-26. 19. Igor Yu. Vlasenko. Topological invariants of equipotential foliation of the Green's function of the Julia set. // Proc. Intern. Geom. Center 2014 7(4). pp. 7-11. 20. Igor Yu. Vlasenko. On the topological conjugacy of two-dimensional homogeneous inner mappings. // Proc. Intern. Geom. Center 2015 8(1). pp. 24-33. 21. I. Yu. Vlasenko. An Example of Neutrally Nonwandering Points for the Inner Mappings that are Not Neutrally Recurrent // Ukrainian Mathematical Journal vol. 67, pages 1159–1163 (2016) 22. Vlasenko I. Yu. Criterion of topological conjugacy for homogeneous mappings of Rn. // Bulletin of Taras Shevchenko National University of Kyiv. Series: Phys. Math. 2015, issue 2, pp. 14-17. 23. E. Polulyakh, V. Sharko, I. Vlasenko. Discretization of Second Lyapunov Method // Qualitative Theory of Dynamical Systems. 2015, vol. 14. issue 2, pp. 1-24. 24. Igor Yu. Vlasenko, Tatiana V. Rybalkina. On the topological conjugacy for non-invertible inner mappings of the wandering cylinder with a simple fundamental neighborhood of type II. // Proceedings of Intsitute of Mathematics of NAS of Ukraine, 12, no. 6 (2015) 146-163 (In Russian). 25. Igor Yu. Vlasenko, Dmitry A. Goltsov. On the topological conjugacy classes of quadratic homogeneous inner polynomial mappings // Proceedings of Intsitute of Mathematics of NAS of Ukraine, 12, no. 6 (2015) 68-88 (In Russian). 26. Igor Yu. Vlasenko. Open finite-to-one functions on open topological graphs. // Proc. Intern. Geom. Center 2020 13(3). pp. 58-63. c) Papers published in Conference Proceedings Vlasenko I., On the topological classification of Morse-Smale diffeomorphisms on 2-manifolds // 6-th Kravchuk conference. Kiev, 1997. pp. 81. Proceedings of the International Conference. Kiev, 1997, p. 81. Vlasenko I., On the topological classification of structurally stable diffeomorphisms on 2-manifolds // Low-Dimensional Topology and Combinatorial Group Theory. Chelyabinsk, July, 31 - August 7, 1999: Proceedings of the International Conference. Kiev, 2000, pp. 319-324. Vlasenko I., Strange attractors in complex dynamics // Complex Analysis and its applications. Lviv, May, 26 - 29, 2003: Proceedings of the International Conference. Lviv, 2003, pp. 19. Vlasenko I., On roots and commutants of Morse-Smale diffeomorphisms on surfaces. // Proceedings of 5-th Pogorelov international conference on geometry and topology, Cherkasy. 2003 Vlasenko I., On roots from Morse-Smale diffeomorphisms on surfaces. // Proceedings of international conference "Geometry in Odessa -- 2004. Differential Geometry and its applications", Odessa, 2004. Vlasenko I., Polulyakh E., Examples of topological limits of smooth manifolds that allow a Birkhoff Center without limit trajectories. // Proceedings of international conference "Geometry in Odessa – 2006. Differential Geometry and its applications", Odessa, 2006. Igor Vlasenko, On the set of $C^r$-weekly nonwandering points //Proceedings of the The 4th International Colloquium "Mathematics in Engineering and Numerical Physics" October 6-8, 2006, Bucharest, Romania I. Vlasenko, On Birkhoff center without limit points // Proceedings of the M.M.Postnikov memorial conference "Algebraic Topology: old and new", Stefan Banach International Mathematical Center, Bedlewo, Poland, 18-24 June 2007 I. Vlasenko. The set of $r$-weakly periodic points and proper disturbances. // Proceedings of international conference "Bogolubov Readings-2007" dedicated to 90th anniversary of Yu. O. Mitropolskiy. Zhitomir, 2007. Vlasenko I., Example of an exotic Birkhoff center. // Proceedings of international conference "Differential Equations and Topology" dedicated to the Centennial Anniversary of L.~S.~Pontryagin, Moscow, 2008. Vlasenko I., Dynamics of Trokhimchuk inner mappings. // Proceedings of international conference "Geometry in Large, and Topology and their applications" dedicated to the 90th Anniversary of A.~V.~Pogorelov, Kharkov, 2009. Vlasenko I., On the dynamics of Trokhimchuk inner mappings. // Proceedings of Ukrainian Mathematical Congress-2009 dedicated to the Centennial Anniversary of M.~M.~Bogolubov, Kiev, 2009. Vlasenko I., On the dynamics of inner mappings. // Proceedings of international conference "Geometry in Odessa - 2010. Differential Geometry and its applications", Odessa, 2010. d) preprints I. Vlasenko, S.Maksimenko. Roots from homeomorphisms and diffeomorphisms of manifolds. // --- Kiev, 2004. --- 64 p. --- (Preprint / NAN of Ukraine. Inst. Of mathematics; 2004.8) I. Vlasenko, E. Polulyah. On iteration stability of the Birkhoff center. // --- Kiev, 2005. --- 64 p. --- (Preprint / NAN of Ukraine. Inst. Of mathematics; 2005.7) e) e-prints I. Vlasenko, Complete invariant for two-dimensional Morse-Smale diffeomorphisms. e-Print, math.DS/9812063 ( 40 p.) f) Papers submitted to referred journals PARTICIPATION AT CONFERENCES International Online Conference Algebraic and Geometric Methods of Analysis dedicated to the memory of Yuriy Trokhymchuk (17.03.1928 - 18.12.2019). May 25-28, Одеса, 2021, "Morse theory and its applications" dedicated to the memory and 70th anniversary of V. Sharko, Kyiv, September 25-28, 2019. "Algebraic and geometric methods of analysis" May 28 - June 3, 2019, Odesa. "Dynamics, Bifurcations and Strange Attractors" Nizhny Novgorod, July 2-9, 2017 "Algebraic and geometric methods of analysis", May 31 - June 5, 2017, Odesa "Modern Advances in Geometry and Topology" in honor of professor A. A. Borisenko for his 70th birthday Ukraine, Kharkiv, September 12-16, 2016 International conference "Dynamics, Bifurcations and Strange Attractors" Nizhny Novgorod, July 18-22, 2016 International conference "Dynamics, Bifurcations and Strange Attractors" Nizhny Novgorod, 2015 International conference “CDC – 2015". Ukraine, Kyiv, 2015. International conference “Geometry in Odessa – 2014. Differential Geometry and its applications”. Ukraine, Odessa, 2014. International conference “Geometry in Odessa – 2013. Differential Geometry and its applications”. Ukraine, Odessa, 2013. International conference “CDC – 2012". Ukraine, Kyiv, 2012. International conference “Geometry in Odessa – 2012. Differential Geometry and its applications”. Ukraine, Odessa, 2012. International conference “Geometry in Odessa – 2010. Differential Geometry and its applications”. Ukraine, Odessa, 2010. "Ukrainian Mathematical Congress - 2009" dedicated to M.~M.~Bogolyubov 90th anniversary. Ukraine, Kiev, 2009. International conference "Geometry, Topology and their applications" in memory of Aleksei Vasilyevich Pogorelov for his 90th birthday anniversary. Ukraine, Kharkiv, 2009. International conference "Differential equations and topology", dedicated to L.~S.~Pontryagin 100th anniversary. Moskow, 2008. International conference "Bogolyubov Readings 2007", dedicated to Yu. O. Mitropolskiy 90th anniversary. Ukraine, Zhitomir, 2007. M.M.Postnikov memorial conference "Algebraic Topology: old and new", Stefan Banach International Mathematical Center, Bedlewo, Poland, 18-24 June 2007 The 4th International Colloquium "Mathematics in Engineering and Numerical Physics", October 6-8, 2006, Bucharest, Romania International conference “Geometry in Odessa – 2006. Differential Geometry and its applications”. Ukraine, Odessa, 2006. VI Pogorelov international conference on geometry and topology. Cherkasy 2005. Summer School and Conference on Dynamical Systems. Abdus Salam International Centre for Theoretical Physics, Trieste, Italy. 18 July-6 August 2004. International conference 'Geometry in Odessa -- 2004. Differential Geometry and its applications', Odessa, 2004. Workshop on dynamical systems. Warwick University, Coventry, 2003. Complex Analysis and its applications. Lviv, May, 26 - 29, 2003. V Pogorelov international conference on geometry and topology. Cherkasy 2003. 1st Ukrainian Mathematical Congress, Kiev, 2001. Andronov Conference, Russia, N. Novgorod. 2001 3rd European Mathematical Congress, Barselona, 2000 Low-Dimensional Topology and Combinatorial Group Theory. Chelyabinsk, July, 31 - August 7, 1999 6-th Kravchuk conference, Kiev, 1997.