Papers

Preprints

Characterising blenders via covering relations and cone conditions; with Bernd Krauskopf, Hinke M. Osinga and Piotr Zgliczyński (preprint), code
Oscillatory collision approach in the Earth-Moon restricted three body problem; with Aleksander Pasiut, (preprint), code

Papers

Breakdown of homoclinic orbits to L3: Nonvanishing of the Stokes constant; with Inmaculada Baldomá, Mar Giralt and Marcel Guardia, (preprint), code, DCDS early access.
Computer assisted proofs for transverse collision and near collision orbits in the restricted three body problem; with Shane Kepley and Jason D. Mireles James (preprint), code for the proof of Theorems 1, 2, 3, code for the proof of Theorems 4, 5. J. of Differential Equations, 366 (2023) 132–191.
Arnold Diffusion, Quantitative Estimates and Stochastic Behavior in the Three-Body Problem; with Marian Gidea, Communications on Pure and Applied Mathematics, 76 (2023) 616-681 (Open Access). code
Breakdown of heteroclinic connections in the analytic Hopf-Zero singularity: Rigorous computation of the Stokes constant; with Inmaculada Baldomá, Marcel Guardia and Tere M. Seara; Journal of Nonlinear Science (2023) 33:28, code
Computer Assisted Proof of Drift Orbits Along Normally Hyperbolic Manifolds II: Application to the Restricted Three Body Problem; with Natalia Wodka, Commun Nonlinear Sci Numer Simulat. 111 (2022) 106424 (preprint) code
Oscillatory Motions and Parabolic Manifolds at Inﬁnity in the Planar Circular Restricted Three Body Problem; with Marcel Guardia, Pau Martin, Tere Seara and Piotr Zgliczyński, J. of Differential Equations, 320 (2022) 316–370 (preprint) code
Computer assisted proof of drift orbits along normally hyperbolic manifolds, with J. Gonzalez, J-P Marco and J. D. Mireles James, Commun Nonlinear Sci Numer Simulat 106 (2022) 105970, code (preprint)
Computer Assisted Proofs of Two-Dimensional Attracting Invariant Tori for ODEs; with E. Fleurantin and J.D. Mireles James; DCDS A 2020, 40(12): 6681-6707
Persistence of normally hyperbolic invariant manifolds in the absence of rate conditions; with Hieronim Kubica, Nonlinearity 33 (2020) 4967–5005 (preprint)
Computer assisted proof of the existence of the Lorenz attractor in the Shimizu-Morioka system; with Dmitry Turaev and Piotr Zgliczyński, Nonlinearity 31 (2018) 5410–5440 (preprint) code
Beyond the Melnikov method II: multidimensional setting; with Piotr Zgliczyński, Journal of Differential Equations Volume 265, Issue 9, 5 November 2018, Pages 3988-4015 (preprint) code
Computer assisted proof of Shil’nikov homoclinics: with application to the Lorenz-84 model; with Anna Wasieczko-Zając, SIAM J. Appl. Dyn. Syst. Vol. 16, No. 3, pp. 1453–1473 code
Validated Computation of Heteroclinic Sets; with Jason D. Mireles James, SIAM J. Appl. Dyn. Syst. Vol. 16, No. 1, (2017) pp. 375–409 code
Arnold Diffusion in the Restricted Three-Body Problem: Mechanism and Numerical Verification; with Marian Gidea and Rafael de la Llave, Nonlinearity 30 (2017) 329–360. (preprint)
Beyond the Melnikov method: a computer assisted approach; with Piotr Zgliczyński, J. of Differential Equations 262, Issue 1, 5 January 2017, Pages 365–417 (preprint)
Geometric Proof of Strong Stable/Unstable Manifolds, with Application to the Restricted Three Body Problem, with Anna Wasieczko-Zając, Topological Methods in Nonlinear Analysis, Vol. 46, No. 1, 2015, 363–399 (preprint)
Geometric proof for normally hyperbolic invariant manifolds; with Piotr Zgliczyński, J. of Differential Equations, Vol. 259, Issue 11, 5 December 2015, Pages 6215–6286 (preprint)
Hedging Conditional Value at Risk with options, European Journal of Operational Research 242 (2015) 688-691 (preprint)
Computer assisted existence proofs of Lyapunov orbits at L2 and transversal intersections of invariant manifolds in the Jupiter-Sun PCR3BP, SIAM J. Appl. Dyn. Syst. 11 (2012), no. 4, 1723-1753.
Computer assisted proof for normally hyperbolic invariant manifolds; with Carles Simó. Nonlinearity 25 (2012), no. 7, 1997–2026 (preprint) (code)
Existence of a Center Manifold in a Practical Domain Around L1 in the Restricted Three Body Problem; with Pablo Roldan. SIAM J. Appl. Dyn. Syst. 11, pp. 285-318.
Transition Tori in the Planar Restricted Elliptic Three Body Problem; with Piotr Zgliczyński. Nonlinearity 24 (2011) 1395-1432. (preprint)
Cone Conditions and Covering Relations for Topologically Normally Hyperbolic Invariant Manifolds; with Piotr Zgliczyński, Discrete and Continuous Dynamical Systems A. Vol. 30, No 3, July 2011, pp. 641–670. (preprint)
Covering Relations and the Existence of Topologically Normally Hyperbolic Invariant Sets, Discrete and Continuous Dynamical Systems A. Vol. 23, N. 3, (March 2009), pp 705-725. (preprint)
Covering Relations and Non-autonomous Perturbations of ODEs; with Piotr Zgliczyński, Discrete and Continuous Dynamical Systems A. Vol 14, N. 2, (Feb 2006), pp. 281–293. (preprint)
Isolating segments for Caratheodory systems and existence of periodic solutions; with Klaudiusz Wójcik, Proc. Amer. Math. Soc. 131 (2003), 2443-2451.

Books

Numerical Methods in Finance with C++; with Tomasz Zastawniak, Cambridge University Press 2012.
Portfolio Theory and Risk Management; with Peter E. Kopp, Cambridge University Press 2014.

PhD Thesis

Arnold diffusion in the planar restricted elliptic three body problem; at the Institute of Mathematics, Jagiellonian University, Kraków, October 2005.

Habilitation

Topological and Geometric Methods for Normally Hyperbolic Invariant Manifolds in Dynamical Systems at Institute of Mathematics, Jagiellonian University, Kraków, March 2016.

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