Projects and Publications

Projects

Between 2019 and 2024, the staff of the Department of Differential Equations (DDE) led 12 projects funded by external agencies.

Projects funded by the National Science Centre

  • - M. Capiński: Diffusion in the N-body Problem (OPUS 21)
  • - J. Boroński: Topological and Dynamical Properties in Parameterized Families of Non-Hyperbolic Attractors: The Inverse Limit Approach (SONATA BIS 9)
  • - P. Oprocha: Entropy, Shadowing and Attractors (OPUS 18)
  • - O. Karpel: Cantor Dynamical Systems and their Classification (SONATA 15)
  • - M. Capiński: Topological Methods for Diffusion in Dynamical Systems (OPUS 15)
  • - M. Capiński: Arnold Diffusion in the Restricted Three-body Problem (OPUS 11)
  • - J. Boroński: Homogeneity and Minimality in Compact Spaces (SONATA 10)
  • - P. Oprocha: Cantor Dynamical Systems, Interval Maps and Mixing (OPUS 9)

Projects funded by other entities

  • - P. Oprocha: Topological and Measurable Shadowing Properties in Dynamical Systems
  • - J. Boroński: Aperiodic Zero-Dimensional Systems
  • - P. Oprocha: Limit Sets of Discrete Dynamical Systems
  • - K. Ciepliński: Organization of the Dynamics, Equations and Applications Conference

 

Publications

Between 2019 and 2024, DDE staff published over 100 papers. A selection is presented below, while the full list is available in the AGH Authors and Publications Database.

  • - J. Banaśkiewicz; P. Kalita; P. Zgliczyński, Computer-assisted validation of the existence of periodic orbits in the Brusselator system, Adv. Differential Equations 29 (2024), no. 11-12, 815-862.
  • - Ł. Cholewa; P. Oprocha, Renormalization in Lorenz maps - completely invariant sets and periodic orbits, Adv. Math. 456 (2024), Paper No. 109890, 45 pp.
  • - M. Capiński; M. Gidea, Arnold diffusion, quantitative estimates, and stochastic behavior in the three-body problem, Comm. Pure Appl. Math. 76 (2023), no. 3, 616-681.
  • - K. Ciepliński, On perturbations of two general equations in several variables, Math. Ann. 385 (2023), no. 1-2, 921-937.
  • - N. Papageorgiou; A. Pudełko; V. Rădulescu, Non-autonomous (p,q)-equations with unbalanced growth, Math. Ann. 385 (2023), no. 3-4, 1707-1745.
  • - K. Baron; R. Kapica, Strong law of large numbers for iterates of some random-valued functions, Results Math. 77 (2022), no. 1, Paper No. 50, 14 pp.
  • - M. Capiński; M. Guardia; P. Martín; T. M-Seara; P. Zgliczyński, Oscillatory motions and parabolic manifolds at infinity in the planar circular restricted three body problem, J. Differential Equations 320 (2022), 316-370.
  • - J. Činč; P. Oprocha, Parametrized family of pseudo-arc attractors: physical measures and prime end rotations, Proc. Lond. Math. Soc. (3) 125 (2022), no. 2, 318-357.
  • - M. Foryś-Krawiec; J. Hantáková; P. Oprocha, On the structure of α-limit sets of backward trajectories for graph maps, Discrete Contin. Dyn. Syst. 42 (2022), no. 3, 1435-1463.
  • - A. Mahdi; C. Pessoa; J. Ribeiro, Rigid centres on the center manifold of tridimensional differential systems, Proc. Roy. Soc. Edinburgh Sect. A 152 (2022), no. 4, 1058-1080.
  • - T. Banakh; S. Głąb; E. Jabłońska; J. Swaczyna, Haar-I sets: looking at small sets in Polish groups through compact glasses, Dissertationes Math. 564 (2021), 105 pp.
  • - L. Sapa, Parabolic-elliptic system modeling biological ion channels, J. Differential Equations 291 (2021), 1-26.
  • - J. Boroński; J. Činč; X.-C. Liu, Prime ends dynamics in parametrised families of rotational attractors, J. Lond. Math. Soc. (2) 102 (2020), no. 2, 557-579.
  • - Ł. Czech, On entropy and reversibility of pushdown dynamical systems, Topology Appl. 272 (2020), 107061, 15 pp.
  • - V. Vladimirov; S. Skurativskyi, On the spectral stability of soliton-like solutions to a non-local hydrodynamic-type model, Commun. Nonlinear Sci. Numer. Simul. 80 (2020), 104998, 15 pp.
  • - E. Adamus; P. Bogdan; T. Crespo; Z. Hajto, Pascal finite polynomial automorphisms, J. Algebra Appl. 18 (2019), no. 7, 1950124, 10 pp.
  • - J. Brzdęk; K. Ciepliński, A fixed point theorem in n-Banach spaces and Ulam stability, J. Math. Anal. Appl. 470 (2019), no. 1, 632-646.
  • - T. Downarowicz; O. Karpel, Decisive Bratteli-Vershik models, Studia Math. 247 (2019), no. 3, 251-271.
  • - P. Oprocha; P. Potorski; P. Raith, Mixing properties in expanding Lorenz maps, Adv. Math. 343 (2019), 712-755.