My research focuses on the study of three-dimensional conservative systems,
with particular emphasis on the analytical and numerical study of invariant manifolds,
splitting of separatrices, separatrix map, and resonant normal forms.
Publications
- A. Murillo and A. Vieiro. Periodic perturbation of a 3D conservative flow with
a heteroclinic connection to saddle-foci. Communications in Nonlinear Science and Numerical
Simulations, 143, 108620, 2025. https://doi.org/10.1016/j.cnsns.2025.108620.
- A. Kazakov, A. Murillo, A. Vieiro, and K. Zaichikov. Numerical study of
discrete Lorenz-like attractors. Regular and Chaotic Dynamics 29(1), 78–99, 2024. https://doi.org/10.1134/S1560354724010064.
Conferences
- Escuela de Matemáticas de América Latina y del Caribe, Urcuqui, Ecuador.
Invited plenary talk: Periodic perturbation of a 3D conservative flow with a
heteroclinic connection to saddle-focus equilibria. 07/2025.
- XLV Dynamics Days Europe, Thessaloniki, Greece.
Parallel session invited talk: Dynamics of 3D conservative maps near a
normally elliptic invariant curve. 06/2025.
- SIAM Conference on Applications of Dynamical Systems, Denver, USA.
Parallel session invited talk: Periodic forcing of a 3D conservative flow with an
invariant 2-sphere of heteroclinic connections to
saddle-foci. 05/2025.
- RSME’s VII Congress of Young Researchers, Bilbao, Spain.
Parallel session invited talk: Dynamics near a normally elliptic invariant curve
in a 3D volume-preserving map. 01/2025.
- 29th International Conference on Difference Equations and Applications, Paris, France.
Parallel session invited talk: Periodic forcing of a 3D volume-preserving flow
with a bubble of stability. 06/2024.
- Recent Trends in Nonlinear Science, Badajoz, Spain.
Poster: Splitting of 2D invariant manifolds of a periodically
forced 3D volume preserving flow. 01/2024.
- NoLineal, Barcelona, Spain.
Contributed talk: Splitting of 2D invariant manifolds of a periodically
forced 3D volume preserving flow. 06/2023.
- RSME’s VI Congress of Young Researchers, León, Spain.
Parallel session invited talk: Periodic perturbation of a 3D conservative flow
with 2D heteroclínic connection to saddle-foci. 02/2023.
- Ddays, Lleida, Spain.
Poster: Numerical investigation of the dynamics of 3D
volume-preserving flows and maps. 09/2021.
Teaching
- Dynamical systems (2024-2025). Faculty of Mathematics and Computer Science,
Universitat de Barcelona
- Mathematics II (2022). Faculty of Mathematics and Computer Science,
Universitat de Barcelona