Publikacje

Papers in pending

  1. How many simplices are needed to triangulate a Grassmannian?, joint z D. Govc and P. Pavesic, accepted to TMNA, (2020).
  2. On the number of simplices required to triangulate a Lie group, joint with H. Duan and X. Zhao, accepted to Top. & Appl.

Papers already published

  1. Topology of unavoidable complexes, joint with D. Josic, S. Vrecica, R. Zivaljevic, J. Fixed Point Theory Appl. 22 (2020), no. 2, Paper No. 31, 12 pp.
  2. Estimates of covering type and the number of vertices of minimal triangulations, joint z D. Govc and P. Pavesic, Discrete Comput. Geom. 63 (2020), no. 1, 31–48.
  3. Geometrically distinct solutions of variational problems with $O(N)$-symmetry, published on-line , Commun. Contemp. Math. 21 (2019), no. 8, 1850080, 34 pp. https://www.worldscientific.com/doi/abs/10.1142/S0219199718500803
  4. General Bourgin-Yang theorem, Topology Appl. 249 (2018), pp 112–126, joint with Z. Błaszczyk and M. Singh.
  5. $(S^1)^k x (Z_p)^l$ equivariant maps between representation spheres, Bulletin of the Belgian Mathematical Society-Simon Stevin, 24(4) (2017), pp 621–630, joint with Z. Błaszczyk and M. Singh.
  6. Bourgin-Yang versions of the Borsuk-Ulam theorem for the p-toral groups, Journal of Fixed Point Theory and Applications, Volume 19 (Issue 2) (2017), 1427–1437, joint with D. de Mattos and E. dos Santos.
  7. On the regularity of the displacement sequence of an orientation preserving circle homeomorphism, Research and Communications in Mathematics and Mathematical Sciences, Vol. 5, Issue 1, 2015, Pages 11-32, Published Online on May 08, 2015
  8. A definition of the Reeb graph as a sub-complex, Topol. Methods Nonlinear Anal. 45 (2015), no. 1, 287–307, joint with M. Kaluba and N. Silva.
  9. The equivariant topological complexity, Bull. Lond. Math. Soc. 47 (2015), no. 1, 101–117, joint with W. Lubawski.
  10. On the interspike-intervals of periodically-driven integrate-and-fire models, J. Math. Anal. Appl. 423 (2015), no. 1, 456–479, joint with J. Signerska
  11. Critical points of equivariant functions on closed orientable surfaces, Bol. Soc. Mat. Mex. (3) 21 (2015), no. 1, 71–88, joint with G. Gromadzki and J. Jezierski
  12. Displacement sequence of an orientation preserving circle homeomorphism, Dyn. Syst. 29 (2014), no. 2, 153–166, joint with J. Signerska.
  13. Bourgin-Yang version of the Borsuk-Ulam theorem for Z_{p^k}-equivariant maps, Algebraic Geometric Topology, 12 (2012), no. 4, 2245–2258. joint with D. de Mattos and E. dos Santos
  14. Firing map of an almost periodic input function, Discrete Contin. Dyn. Syst., DCDS Suppl., 1032-1041, (2011), joint with J. Signerska.
  15. Conformal actions with prescribed periods on Riemann surfaces, Fund. Math., no. 2, (2011), 169–190, joint with G. Gromadzki.
  16. Periodic points of equivariant maps, Mathematica Scandinavica, 107 (2010) 224-248 joint with J. Jezierski.
  17. A non-smooth three critical points theorem with applications in differential inclusions, Journal of Global Optimization, Volume 46, Issue 1 (2010), 49-62, joint with A. Kristaly, C. Varga.
  18. Homotopical theory of periodic points of periodic homeomorphisms on closed surfaces. Topology Appl. 156 (2009), no. 15, 2527–2536, joint with H. Zhao.
  19. Homotopy minimal periods of holomorphic maps on surfaces, Funct. Approx. Comment. Math. 40 (2009), part 2, 309–326, joint with J. Llibre.
  20. A decomposition formula for equivariant stable homotopy classes, Topological Methods in Nonlinear Analysis, 33 (2009), no. 2, 285–29, joint with C. Prieto.
  21. Wecken property for periodic points on the Klein bottle, Topol. Methods Nonlinear Anal. 33 (2009), no. 1, 51–64, joint with J. Jezierski, E. Keppelmann.
  22. Estimates of the topological entropy from below for continuous self-maps on some compact manifolds, Discrete and Continuous Dynamical Systems Series A, 21, 501-512,(2008), joint with F. Przytycki.
  23. Periodic solutions of symmetric autonomous Newtonian systems, Jour. Diff. Equations, 244 , Issue 4, (February 2008), 916-944, joint with C. Prieto, S. Rybicki.
  24. The sets of homotopy periods for maps of three dimensional solvmanifolds, Topology and Applications, Vol. 155, (2008), 923-945, joint with J. Jezierski, E. Keppelmann.
  25. Multiplicity of symmetrically distinct sequences of solutions of quasi-linear problem in R^N, NoDEA (Nonlin. Diff. Equat. and Appl.), 2008; 15 (1-2), 209-226, joint with A. Kristaly.
  26. Entropy conjecture for nilmanifolds, Israel, Journal of Math., Volume 165, No.1, June (2008), 349-379, joint with F. Przytycki.
  27. Periodic segment implies infinitely many periodic solutions, Proc. Amer. Math. Soc, 135, (2007), 2637-2647, joint with K. Wójcik.
  28. Positive oriented periodic solutions of the first order complex ODE with polynomial nonlinear part, Archives of Inequalities and Applications, 2006 (2006), Article ID 42908, 22 pp, joint with A. Borisovich.
  29. Indices of iterations of planar maps, Folia Mathematica – Lódź, 12, No 1, (2005), 3-13, joint with G. Graff.
  30. Computation of the equivariant 1-stem by a decomposition of equivariant stable homotopy classes, Nonlinear Analysis, Vol 63, (4), (2005), 513-524, joint with C. Prieto.
  31. A symmetry implies a chaos for a sphere map, Bulletin of the Brazilian Mathematical Society, (NS), 36 (2005), no. 2, 205-224, joint with J. Jezierski.
  32. Symmetry breaking solutions of nonlinear elliptic systems, Topological Methods in Nonlinear Analysis, Vol. 26, (2005), 189-201, joint with J. Bracho, M. Clapp.
  33. Homotopy minimal periods, a charter of a book, Handbook of Topological Fixed Point Theory, Editor(s): R. F. Brown, M. Furi, L. Górniewicz and B. Jiang, Springer, Dordrecht, (2005), 129-170.
  34. Homotopy minimal periods for NR-solvmanifolds maps, Topology and Applications, Volume 144, Issues 1-3, 2004, 29-49, joint with J. Jezierski i J. Kędra.
  35. The unstable equivariant fixed point index and the equivariant degree, J. London Math. Soc, Vol. 69 (2), (2004), 214-230, joint with C. Prieto.
  36. Homotopical dynamics (a survey article); Universitatis Iagiellonicae Acta Mathemat-ica, FASC. IIIL, 2003.
  37. Periodic solutions of nonlinear problems with with holomorphic type of the nonlinearity; Topology Methods, Variational Methods and their Applications, Proc. ICM 2002 Satellite Conference on Nonlinear Functional Analysis, Taiyuan August 2002, edited by H. Brezis, P. H. Rabinowitz, Shuje Li, Scientific World Publ., Singapore, 2003.
  38. Homotopy minimal periods for maps of three dimensional nilmanifolds; Pacific J. of Math., Vol. 209, No.1, (2003), 85-101, joint with J. Jezierski..
  39. Generalized Lefschetz numbers of equivariant maps; Osaka Journal of Math., 39, (2002), 821-841 – joint with C. Prieto.
  40. Algorithm for deriving homotopy minimal periods of nilmanifold and solvmanifold map, Proc. of III-rd National Conference on Nonlinear Analysis, Lecture Notes of the Juliusz Schauder Center for Nonlinear Studies, Vol. 3, (2002), 109-130 – joint with R. Komendarczyk.
  41. Homotopy minimal periods for nilmanifold maps, Mathematische Zeitschrift, 239, (2002), 381- 414 – joint with J. Jezierski.
  42. Periodic solutions of nonlinear problems with positive oriented periodic coefficients, Variational and Topological Methods in the Study of Nonlinear Phenomena, Editors – Benci, Cerami, Degiovanni, Fortunato, Giannoni, and Micheletti, Birkhauser, Series – PNLDE, Vol. 49, (2002), 43-64.
  43. Multiplicity of periodic solutions for the planar polynomial equation, Nonlinear Analysis, 43 (2001), 217-231 – joint with A. Borisovich .
  44. The Borsuk-Ulam property for cyclic groups, Topological Methods in Nonlinear Analysis, Vol. 16, (2000), 65-72 – joint with M. Izydorek
  45. An asymptotic formula for the number of bifurcating solutions for the equation $-\Delta u=\mu f(u)$, Functiones et Approx., XXVIII, (2000), 195-200 – joint with W. Krawcewicz.
  46. Essential equivariant maps and Borsuk-Ulam theorems, J. London Math. Soc., (2) 61 (2000), no. 3, 950-960. – joint with M. Clapp.
  47. A multiplicity result for a system of real integral equations by use of the Nielsen number, Banach Center Publishing, Nielsen theory and Reidemeister Torsion, vol. 49, 1999, 9-18, – joint with A. Borisovich , Z. Kucharski.
  48. Finding periodic points of a map by use of a $k$-adic expansion, Discrete and Continuous Dynamical Systems, Vol. 5, No. 3, 1999, 495-514, – joint with M. Przygodzki.
  49. A note on the minimal periods of a homeomorphism of compact surface, Universitatis Iagiellonicae Acta Mathematica, FASC. XXXVI, 1998, 115-119 .
  50. Equivariant category of the free part $G$-manifold and the sphere of spherical harmonics, Kodai Jour. Mathematics, vol. 20 No.2 (1997), 92-106.
  51. Some applications of the Nielsen number to algebraic sets, Proceedings of the Conference: “Topological Methods in Nonlinear Analysis” – Gdañsk, December 95″, GTN – Gdañsk Scientific Society, (1997), 78-90 – joint with A. Borisovich , Z. Kucharski.
  52. A remark on the multiplicity result for a class of nonlinear problems, Proceedings of the Conference: “Topological Methods in Nonlinear Analysis” – Gdañsk, December 95″, GTN – Gdañsk Scientific Society, (1997), 91 -96 – joint with A. Borisovich , Z. Kucharski.
  53. Finding periodic points of smooth mapping using Lefschetz numbers of its iterations, Izviestya Vuzov RRF, vol. 417, No 2, (1997), 86-96.
  54. Bifurcation of the equivariant minimal interfaces in a hydromechanics problem, Abstract and Applied Analysis, vol. 1, No 3, (1996), 291-304 – joint with A. Borisovich .
  55. Equivariant maps between cohomology spheres, Topological Methods in Nonlinear Analysis, vol. 5 No 2, (1995), 279-290 – joint with M. Izydorek
  56. Fixed Point index for equivariant compact maps of $G$- ANR’s, Applied Aspects of Global Analysis; New Development in Global Analysis series, Voronezh University Press, (1994), 74-90 – joint with W. Krawcewicz.
  57. Nielsen number and lower estimate for the number of solutions to a certain system of nonlinear integral equations, Applied Aspects of Global Analysis; New Development in Global Analysis series, Voronezh University Press, (1994), 3 -11 – joint with A. Borisovich, Z. Kucharski .
  58. Borsuk-Ulam theorem for any compact Lie group, the Journal of the London Mathematical Society, vol. 49, (1994), 95- 208.
  59. Global bifurcation of periodic solutions, Topological Methods in Nonlinear Analysis, 1 (1993), 67 – 93. – joint with K. Gêba.
  60. The existence of the linear slice for an orbit of representation in a Banach space, Commentationes Mathematicae, Vol. XXXIII (1993), 65 -72 -joint with J. Jodel .
  61. An S -equivariant degree and the Fuller index, Ann. Math. Pol. L II. (1991), 243 – 280 – joint with G. Dylawerski, K. Gêba. , J. Jodel .
  62. An almost classification of compact Lie group with a Borsuk-Ulam property, Pacific J. of Math., Vol. 144, No. 2, (1990) 299 – 311.
  63. Some remarks on the Lusternik-Schnirelman method for non-differentiable functionals invariant with respect to a finite group action, the Rocky Mountain Jour. of Math., Vol. 20, N. 4, Fall 1990, 1041 – 1049 – joint with W. Krawcewicz.
  64. Lusternik-Schnirelman method for functionals invariant with respect to a finite group action, J. Diff. Equations, 85 (1990), 105 – 124 – joint with W. Krawcewicz.
  65. A G-Lusternik-Schnirelman category of space with an action of a compact Lie group, Topology 28, No. 4 (1989), 403-412.
  66. A Borsuk-Ulam theorem for orthogonal $T^k$ and $Z^k$ actions and applications, J. Math. An. and App., Vol. 137, No. 1, Jan. 1989, 99-121.
  67. Equivariant Morse inequalities, Mathematical Letters of Univ. of Gdañsk, Vol. 6, 1987, 55-60.
  68. Periodic solutions near an equilibrium of a differential equation with a first integral, Rend. Sem. Mat. Univ. Padova, Vol. 77, 1987, 193–206 – joint with A. Parusiñski
  69. On the nonlinear elliptic equations with symmetry, Journal of Math. Anal. and Appl., Vol. 881, No. 1, 1981, 156-181.
  70. The Lefschetz number in equivariant K-theory, Bull. de l’ Acad. Polon. Sci., Vol XXV, No. 9, 1977, 901–906.
  71. A formula for G-Euler characteristic, Bull. de l’Acad. Polon. des Sci. , Vol. XXIII, No. 5, 1975, 565-570.

Books

  1. Elementy Teorii Liczb, (Elements of Number Theory), Scientific Publishing of the Adam Mickiewicz University of Poznań, Poznań, 1999 (in Polish), an improved version of Elementy Teorii Liczb, 1985 – joint with P. Zarzycki.
  2. Elementy Teorii Liczb (Elements of Number Theory), Univ. of Gdañsk Press, Gdañsk, 1985 (in Polish) – joint with P. Zarzycki .
  3. Wstep do Analizy Nieliniowej – First part „Teoria Stopnia”, (manual in Polish), Wydawnictwo Naukowe UAM, 2003, joint with J. Gulgowski.
  4. Homotopy Methods in Topological Fixed and Periodic Points Theory, monograph, Springer , (2006), XI, 319 p., ISBN: 1-4020-3930-1, joint with J. Jezierski.
  5. Elementarna teoria liczb (Elementary number theory), Wydawnictwo Naukowe PWN, (2006), 120 p., ISBN: 83-01-14855-1, (podręcznik – a manual in Polish), joint with P. Zarzycki.