PUBLICATIONS

Books

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).

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.
  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.
  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. --P. 90--96.
  4. Igor Vlasenko, On the complete invariant of Morse-Smale diffeomorphisms on unoriented surfaces. // Uspekhi Mat. Nauk, v. 54, No. 5 (329), 1999. --P. 155--156
  5. Igor Vlasenko, Numerical characteristics on the set of heteroclinic points of Morse-Smale diffeomorphisms on surfaces. // Ukrainian Math. Journal, v. 52, No. 10, 2000. --P. 1412--1417
  6. Igor Vlasenko, Topological properties of periodic components of A-diffeomorphisms. // Ukrainian Math. Journal, v. 54, No. 8, 2002. --P. 1131—1141.
  7. Igor Vlasenko, Topological properties of periodic components of structurally stable diffeomorphisms. // Ukrainian Math. Journal, v. 54, No. 9, 2002. --P. 1190--1199.
  8. Igor Vlasenko, An example of 2-dimentional attractor in 4-manifold based on expanding maps of tori. // Topology and geometry: Proceedings of UMK-2001. ---Kiev: Inst. of Math., 2003. --P. 50--53.
  9. I. Vlasenko, An example of irreversible Williams' solenoid. // Matematychni Studii, v. 21, No. 1, 2004. --P. 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. --P. 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. -- P 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. -P. 373--389. (In Russian)
  15. I. Yu. Vlasenko. Dynamics of inner maps // Nonlinear Oscillations. V.14 No. 2 2011 pp. 181-186
  16. I. Yu. Vlasenko. Factor-homeomorphism of Inner Epimorphism. // Proceedings of Ukrainian Math Congress - 2009. Section 2. Topology and Geometry. -- Kyiv - 2011. --P. 29--37.
  17. I. Yu. Vlasenko. Dynamics of inner maps. // Nonlinear Oscillations. V.14 No. 2 2011 pp. 181-186
    doi: https://doi.org/10.1007/s11072-011-0150-4 | sjr: Q4
  18. I. Yu. Vlasenko. Classification of the Regular Components of Two-Dimensional Inner Maps // Ukrainian Mathematical Journal vol. 66, pp. 42–49 (2014)
    doi: https://doi.org/10.1007/s11253-014-0910-2 | sjr: Q3
  19. Igor Yu. Vlasenko. Abundance of topological conjugacy classes for wandering sets of inner mappings // Proc. Intern. Geom. Center 2014 7(3). --P. 21--26.
    doi: https://doi.org/10.15673/2072-9812.3/2014.40229
  20. Igor Yu. Vlasenko. Topological invariants of equipotential foliation of the Green's function of the Julia set. // Proc. Intern. Geom. Center 2014 7(4). --P. 7--11.
    doi: https://doi.org/10.15673/2072-9812.4/2014.41431
  21. Igor Yu. Vlasenko. On the topological conjugacy of two-dimensional homogeneous inner mappings. // Proc. Intern. Geom. Center 2015 8(1). --P. 24-33.
    doi: https://doi.org/10.15673/2072-9812.1/2015.49278
  22. 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)
    doi: https://doi.org/10.1007/s11253-016-1143-3 | sjr: Q3
  23. Vlasenko I. Yu. Criterion of topological conjugacy for homogeneous mappings of Rn. // Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics 2015, issue 2, --P. 14-17.
  24. E. Polulyakh, V. Sharko, I. Vlasenko. Discretization of Second Lyapunov Method // Qualitative Theory of Dynamical Systems. 2015, vol. 14. issue 2, pp. 1-24.
    doi: http://dx.doi.org/10.1007/s12346-015-0156-x | sjr: Q3
  25. 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).
  26. 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).
  27. Igor Yu. Vlasenko. Open finite-to-one functions on open topological graphs. // Proc. Intern. Geom. Center 2020 13(3). --P. 58-63.
    doi: https://doi.org/10.15673/tmgc.v13i3.1880

Papers published in Conference Proceedings

  1. Vlasenko I., On the topological classification of Morse-Smale diffeomorphisms on 2-manifolds // 6-th Kravchuk conference. Kiev, 1997. --P. 81. Proceedings of the International Conference. -- Kiev, 1997, p. 81.
  2. 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.
  3. 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..
  4. 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
  5. 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.
  6. 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.
  7. 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
  8. 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
  9. 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.
  10. 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., – Moscow, 2008.
  11. 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. &ndash Kharkov, 2009.
  12. 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. &ndash Kiev, 2009.
  13. Vlasenko I., On the dynamics of inner mappings. // // Proceedings of international conference “Geometry in Odessa – 2010. Differential Geometry and its applications”, Odessa, 2010.

Preprints

  1. I. Vlasenko, S.Maksimenko. Roots from homeomorphisms and diffeomorphisms of manifolds. // --- Kiev, 2004. --- 64 p. --- (Preprint / NAN of Ukraine. Inst. Of mathematics; 2004.8)
  2. 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-prints

  1. I. Vlasenko, Complete invariant for two-dimensional Morse-Smale diffeomorphisms. e-Print, math.DS/9812063 (40 p.)

to appear

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