Assistant professor

Nicolaus Copernicus University in Toruń
Faculty of Mathematics & Computer Science
ul. Chopina 12/18,  87-100 TORUŃ, POLAND
E-mail address: robo@mat.umk.pl
Office: room F 304

Scientific interests

  • Topological methods in nonlinear analysis (topological degree, fixed point index)
  • Qualitative theory of (nonautonomous) dynamical systems
  • Numerical discretization theory
  • Differential inclusions and nonsmooth analysis

Publications

  1. R. Skiba, On the Lefschetz fixed point theorem for multivalued weighted mappings, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 40, 2001, 201-214.
  2. R. Skiba, Topological essentiality for multivalued weighted mappings, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 41, 2002, 131-145.
  3. J. Pejsachowicz, R. Skiba, Fixed point theory of multivalued weighted maps, Handbook of Topological Fixed Point Theory, Springer, Dordrecht, 2005, 217-263.
  4. R. Skiba, Graph-approximation of multivalued weighted maps, Topol. Methods Nonlinear Anal., 29, 2007, 119-161.
  5. R. Skiba, Fixed points of multivalued weighted maps, Lecture Notes in Nonlinear Analysis, vol. 9, Juliusz Schauder Center for Nonlinear Studies,Nicolaus Copernicus University, Toruń 2007, 1-148.
  6. R. Skiba, M. Ślosarski, On a generalization of absolute neighborhood retratcs, Topology and its Applications, 156 (2009) 697-709.
  7. W. Kryszewski, R. Skiba, A cohomological index of Fuller type for set-valued dynamical systems, Nonlinear Analysis, Theory, Methods & Applications, 75 (2012), 684-716.
  8. J. Pejsachowicz, R. Skiba, Global bifurcation of homoclinic trajectories of discrete dynamical systems, Central European Journal of Mathematics, 10(6) 2012, 2088-2109.
  9. J. Pejsachowicz, R. Skiba, Topology and homoclinic trajectories of discrete dynamical systems, Discrete Contin. Dyn. Syst. S, 6(4), 2013, 1077-1094.
  10. R. Skiba, Applications of weighted maps to periodic problems of autonomous differential equations, Topol. Methods Nonlinear Anal., 42(1) 2013, 9-49.
  11. R. Skiba, A cohomological index of Fuller type for parameterized set-valued maps in normed spaces, Central European Journal of Mathematics, 12(8) 2014, 1164-1197.
  12.  R. Skiba, N. WaterstraatThe Index Bundle and Multiparameter Bifurcation for Discrete Dynamical Systems, DCDS-A, 37(11), 2017, 5603-5629 (arXiv:1612.05837).
  13. C. Potzsche, R. Skiba, Global Continuation of Homoclinic Solutions, Zeitschrift fur Analysis und ihre Anwendungen, Volume 37 (2018), 159-187,DOI: 10.4171/ZAA/1608.
  14. C. Potzsche, R. Skiba, A Continuation Principle for Fredholm maps I:Theory and Basics (submitted).
  15. C. Potzsche, R. Skiba, A Continuation Principle for Fredholm maps II: Application to homoclinic solutions (submitted).
  16. R. Skiba, The intersection degree and its applications (in preperation).
  17. R. Skiba,N. Waterstraat, Fredholm theory of discrete dynamical systems and its applications to bifurcation theory (in preperation).

Curriculum vitae

employment

  •     October 2006 - present: assistant professor in the Department of Nonlinear Analysis and Topology, Faculty of Mathematics and Computer Science, NCU
  •     October 2005 - September 2006: assistant in the Department of Nonlinear Analysis and Topology, Faculty of Mathematics and Computer Science, NCU

scientific degrees

  •     PhD in Mathematics, Nicolaus Copernicus University, February 2006, adviser: prof. dr hab. L. Górniewicz
  •     MSc in Mathematics, Nicolaus Copernicus University, June 2001, adviser: prof. dr hab. L. Górniewicz