Symmetric Heteroclinic Connections in the Michelson System: A Computer Assisted Proof. - Daniel Wilczak (SIAM J. Appl. Dyn. Syst., 2005)

The Existence of Shilnikov Homoclinic Orbits in the Michelson System: A Computer Assisted Proof. - Daniel Wilczak (Found. Comput. Math., 2006)

Period Doubling in the Rössler System - A Computer Assisted Proof. - Daniel Wilczak; Piotr Zgliczynski (Found. Comput. Math., 2009)

Computer Assisted Proof of the Existence of Homoclinic Tangency for the Hénon Map and for the Forced Damped Pendulum. - Daniel Wilczak; Piotr Zgliczynski (SIAM J. Appl. Dyn. Syst., 2009)

Uniformly Hyperbolic Attractor of the Smale-Williams Type for a Poincaré Map in the Kuznetsov System. - Daniel Wilczak (SIAM J. Appl. Dyn. Syst., 2010)

An implicit algorithm for validated enclosures of the solutions to variational equations for ODEs. - Irmina Walawska; Daniel Wilczak (Appl. Math. Comput., 2016)

Coexistence and Dynamical Connections between Hyperchaos and Chaos in the 4D Rössler System: A Computer-Assisted Proof. - Daniel Wilczak; Sergio Serrano; Roberto Barrio (SIAM J. Appl. Dyn. Syst., 2016)

Connecting Orbits for a Singular Nonautonomous Real Ginzburg-Landau Type Equation. - Daniel Wilczak; Piotr Zgliczynski (SIAM J. Appl. Dyn. Syst., 2016)

Systematic Computer-Assisted Proof of Branches of Stable Elliptic Periodic Orbits and Surrounding Invariant Tori. - Daniel Wilczak; Roberto Barrio (SIAM J. Appl. Dyn. Syst., 2017)

Validated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systems. - Irmina Walawska; Daniel Wilczak (Commun. Nonlinear Sci. Numer. Simul., 2019)

CAPD: : DynSys: A flexible C++ toolbox for rigorous numerical analysis of dynamical systems. - Tomasz Kapela; Marian Mrozek; Daniel Wilczak; Piotr Zgliczynski (Commun. Nonlinear Sci. Numer. Simul., 2021)

Recent advances in a rigorous computation of Poincaré maps. - Tomasz Kapela; Daniel Wilczak; Piotr Zgliczynski (Commun. Nonlinear Sci. Numer. Simul., 2022)

Computer assisted proofs in dynamical systems. - Maciej J. Capinski; Jason D. Mireles-James; Warwick Tucker; Daniel Wilczak; Jan Bouwe van den Berg (Commun. Nonlinear Sci. Numer. Simul., 2023)

Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line II. - Daniel Wilczak; Piotr Zgliczynski (CoRR, 2024)

Make Interval Bound Propagation great again. - Patryk Krukowski; Daniel Wilczak; Jacek Tabor; Anna Bielawska; Przemyslaw Spurek (CoRR, 2024)

Continuation and bifurcations of periodic orbits and symbolic dynamics in the Swift-Hohenberg equation. - Jakub Czwórnóg; Daniel Wilczak (Commun. Nonlinear Sci. Numer. Simul., 2025)

Self-consistent bounds method for dissipative PDEs. - Daniel Wilczak; Piotr Zgliczynski (CoRR, 2025)

A mechanism for growth of topological entropy and global changes of the shape of chaotic attractors. - Daniel Wilczak; Sergio Serrano; Roberto Barrio (CoRR, 2025)