dr hab. Daniel Wilczak, prof. UJ

Jednostki:

  • Wydział Matematyki i Informatyki UJ
  • Instytut Informatyki i Matematyki Komputerowej
  • Katedra Matematyki Obliczeniowej

Habilitacja  Otwarcie: 2011-01-27, Zamknięcie: 2011-10-06

Publikacje:

28.
Jakub Czwórnóg, Daniel Wilczak
Continuation and bifurcations of periodic orbits and symbolic dynamics in the Swift-Hohenberg equation, Communications in Nonlinear Science and Numerical Simulation vol. accepted (2025),
27.
Daniel Wilczak, Maciej Capiński, Warwick Tucker, Jason D. Mireles James, Jan Bouwe van den Berg
Computer assisted proofs in dynamical systems, Communications in Nonlinear Science and Numerical Simulation vol. 118 (2023), 106998
26.
Tomasz Kapela, Daniel Wilczak, Piotr Zgliczyński
Recent advances in a rigorous computation of Poincaré maps, Communications in Nonlinear Science and Numerical Simulation vol. 110 (2022), 106366
25.
Tomasz Kapela, Marian Mrozek, Daniel Wilczak, Piotr Zgliczyński
CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems , Communications in Nonlinear Science and Numerical Simulation vol. 101 (2021), 105578
24.
Roberto Barrio, Daniel Wilczak
Distribution of stable islands within chaotic areas in the non-hyperbolic and hyperbolic regimes in the Henon-Heiles system, Nonlinear Dynamics vol. 102 (2020), 403-416
23.
Daniel Wilczak, Piotr Zgliczyński
A geometric method for infinite-dimensional chaos: Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line, Journal of Differential Equations vol. 269 (2020), 8509-8548
22.
Irmina Walawska, Daniel Wilczak
Validated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systems, Communications in Nonlinear Science and Numerical Simulation vol. 74C (2019), 30-54
21.
Roberto Barrio, Daniel Wilczak
Systematic Computer-Assisted Proof of Branches of Stable Elliptic Periodic Orbits and Surrounding Invariant Tori, SIAM Journal on Applied Dynamical Systems vol. 16 (2017), 1618-1649
20.
Irmina Walawska, Daniel Wilczak
An implicit algorithm for validated enclosures of the solutions to variational equations for ODEs, Applied Mathematics and Computation vol. 291 (2016), 303-322
19.
Daniel Wilczak, Piotr Zgliczyński
Connecting Orbits for a Singular Nonautonomous Real Ginzburg--Landau Type Equation, SIAM Journal on Applied Dynamical Systems vol. 15 (2016), 495-525
18.
Roberto Barrio, Sergio Serrano, Daniel Wilczak
Coexistence and Dynamical Connections between Hyperchaos and Chaos in the 4D Rössler System: A Computer-Assisted Proof, SIAM Journal on Applied Dynamical Systems vol. 15 (2016), 356-390
17.
Roberto Barrio, María Angeles Martinez, Sergio Serrano, Daniel Wilczak
When chaos meets hyperchaos: 4D Rössler model, Physics Letters, Section A: General, Atomic and Solid State Physics vol. 379 (2015), 2300-2305
16.
Daniel Wilczak, Piotr Zgliczyński
C^r-Lohner algorithm, Schedae Informaticae vol. 20 (2011), 9-46
15.
Daniel Wilczak
Uniformly hyperbolic attractor of the Smale-Williams type for a Poincaré map in the Kuznetsov system, SIAM Journal on Applied Dynamical Systems vol. 9 (2010), 1263-1283
14.
Daniel Wilczak, Piotr Zgliczyński
Computer assisted proof of the existence of homoclinic tangency for the Henon map and for the forced-damped pendulum, SIAM Journal on Applied Dynamical Systems vol. 8 (2009), 1632-1663
13.
Warwick Tucker, Daniel Wilczak
A rigorous lower bound for the stability regions of the quadratic map, Physica D: Nonlinear Phenomena vol. 238 (2009), 1923-1936
12.
Daniel Wilczak, Piotr Zgliczyński
Period doubling in the Rössler system - a computer assisted proof, Foundations of Computational Mathematics vol. 9 (2009), 611-649
11.
Daniel Wilczak
Abundance of heteroclinic and homoclinic orbits for the hyperchaotic Rössler system, Discrete and Continuous Dynamical Systems - Series B vol. 11 (2009), 1039-1055
10.
Daniel Wilczak
Rigorous numerics for homoclinic dynamics, the Joint Conference of Ascm 2009 and Macis 2009, Coe Lect. Note, 22, Kyushu Univ. Fac. Math., Fukuoka (2009), 301-305
9.
Hiroshi Kokubu, Daniel Wilczak, Piotr Zgliczyński
Rigorous verification of cocoon bifurcations in the Michelson system, Nonlinearity vol. 20 (2007), 2147-2174
8.
Daniel Wilczak, Piotr Zgliczyński
Topological method for symmetric periodic orbits for maps with a reversing symmetry, Discrete and Continuous Dynamical Systems vol. 17 (2007), 629-652
7.
Daniel Wilczak
The existence of Shilnikov homoclinic orbits in the Michelson system: a computer assisted proof, Foundations of Computational Mathematics vol. 6 (2006), 495-535
6.
Daniel Wilczak
Symmetric homoclinic solutions to the periodic orbits in the Michelson system, Topological Methods in Nonlinear Analysis vol. 28 (2006), 155-170
5.
Daniel Wilczak, Piotr Zgliczyński
Heteroclinic Connections between Periodic Orbits in Planar Circular Restricted Three Body Problem - part II, Communications in Mathematical Physics vol. 259 (2005), 561-576
4.
Daniel Wilczak
Symmetric heteroclinic connections in the Michelson system - a computer assisted proof, SIAM Journal on Applied Dynamical Systems vol. 4 (2005), 489-514
3.
Daniel Wilczak, Piotr Zgliczyński
Heteroclinic Connections between Periodic Orbits in Planar Circular Restricted Three Body Problem - A Computer Assisted Proof, Communications in Mathematical Physics vol. 234 (2003), 37-75
2.
Daniel Wilczak
Chaos in the Kuramoto-Sivashinsky equations - a computer assisted proof, Journal of Differential Equations vol. 194 (2003), 433-459
1.
Daniel Wilczak
Computer assisted proof of chaotic dynamics in the Rössler map, Topological Methods in Nonlinear Analysis vol. 18 (2001), 183-190

Konferencje:

10.
Daniel Wilczak.
The Seventh International Meeting on Celestial Mechanics, Università di Roma, San Martino al Cimino, Włochy, 2017-09-03 - 2018-03-09
9.
Daniel Wilczak.
Rigorous Numerics for Infinite Dimensional Nonlinear Dynamics, BIRS, Banff, Kanada, 2017-05-08 - 2017-05-12
8.
Daniel Wilczak.
9th Small Workshop on Interval Methods, University of Lyon, Lyon, Francja, 2016-06-19 - 2016-06-22
7.
Piotr Zgliczyński, Daniel Wilczak.
Computation in Dynamics, ICERM Brown University, Providence, USA, 2016-04-04 - 2016-04-08
6.
Tomasz Kapela, Daniel Wilczak.
Winter School on Computational Mathematics 2016, WMiI UJ, Będlewo, Polska, 2016-02-07 - 2016-02-13
5.
Tomasz Kapela, Daniel Wilczak, Mateusz Juda, Grzegorz Jabłoński, Jarosław Duda.
DYNAMICS, TOPOLOGY AND COMPUTATIONS 2015 (DyToComp), Stefan Banach International Mathematical Center, Faculty of Mathematics and Computer Science UJ, Będlewo, Polska, 2015-06-15 - 2015-06-20
4.
Daniel Wilczak.
8th Small Workshop on Interval Methods, Charles University in Prague , Praga, Republika Czeska, 2015-06-09 - 2015-06-11
3.
Daniel Wilczak.
Foundations of Computational Mathematics, Society for Foundations of Computational Mathematics, Montevideo, Urugwaj, 2014-12-11 - 2014-12-20
2.
Leszek Gasiński, Piotr Kalita, Tomasz Kapela, Daniel Wilczak, Aleksander Czechowski.
The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications , AIMS, Madryt, Hiszpania, 2014-07-07 - 2014-07-11
1.
Daniel Wilczak.
7th Small Workshop on Interval Methods, Uppsala Universitet, Uppsala, Szwecja, 2014-06-11 - 2014-06-12

Konferencje organizowane:

Doktoranci (po 27 października 2003 roku)

Recenzje (po 27 października 2003 roku)

Granty (realizowane po maju 2009 roku)

TytułRolaRozpoczęcieZakończenie
Metody geometryczne i ścisła numeryka w dynamice układów hamiltonowskichWykonawca2016-07-072019-07-06
Obliczeniowa dynamika topologicznaWykonawca2015-10-012022-09-30
Rozproszone i równoległe algorytmy w Matematyce ObliczeniowejKierownik2011-06-192012-10-19