Arturo Vieiro Yanes

Professor Agregat / Associate Lecturer (UB)
Departament de Matemàtiques i Informàtica.
Universitat de Barcelona
Gran Via, 585, 08007 Barcelona
Telèfon: 93 403 46 87
e-mail: vieiro@maia.ub.es
OrCid ID 0000-0003-2584-2717

I am interested in dynamical systems, with a particular focus on Hamiltonian dynamics and symplectic maps, bifurcation theory, conservative/dissipative chaos, strange attractors and numerical methods tailored to the study of dynamical systems.

Publications Conferences Outreach Useful links Miscellaneous

Publications

A. Murillo and A. Vieiro. Detecting quasi-periodic properties of the splitting of separatrices via simultaneous approximation.
Chaos 36(6):063105, 2026. PDF
V. Gelfreich and A. Vieiro. Nekhoroshev theory and discrete averaging.
Discrete and Continuous Dynamical Systems DCDS-A, 2025. Preprint ArXiv PDF
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 Simulation, 143, 108620, 2025. PDF
V. Gelfreich and A. Vieiro. On exponentially accurate approximation of a near the identity map by an autonomous flow.
Preprint ArXiv
A. Kazakov, A. Murillo, A. Vieiro and K. Zaichikov. Numerical study of discrete Lorenz-like attractors.
Regular and Chaotic Dynamics 29(1), 77--98, 2024. PDF
E. Fontich and A. Vieiro. Dynamics near the invariant manifolds after a Hamiltonian-Hopf bifurcation.
Communications in Nonlinear Science and Numerical Simulation, 117, 106971, 2023. PDF
N. Miguel, C. Simó and A. Vieiro. Escape Times Across the Golden Cantorus of the Standard Map.
Regular and Chaotic Dynamics 27(3), 281--306, 2022. PDF
J.C. Tatjer and A. Vieiro. Dynamics of the QR-flow for upper Hessenberg real matrices.
Discrete & Continuous Dynamical Systems - B 26(3), 1359--1403, 2021. PDF
E. Fontich, C. Simó and A. Vieiro. Splitting of the separatrices after a Hamiltonian-Hopf bifurcation under periodic forcing.
Nonlinearity 32(4), 1440--1493, 2019. PDF Preprint ArXiv
E. Fontich, C. Simó and A. Vieiro. On the ``hidden'' harmonics associated to best approximants due to quasi-periodicity in splitting phenomena.
Regular and Chaotic Dynamics 23(6), 638--653, 2018. PDF
J.D. Meiss, N. Míguel-Baños, C. Simó and A. Vieiro. Accelerator modes and anomalous diffusion in 3D volume-preserving maps.
Nonlinearity 31(12), 5615--5642, 2018. PDF Preprint ArXiv
M. Gonchenko, S. Gonchenko, I. Ovsyannikov and A. Vieiro. On local and global aspects of the 1:4 resonance in the conservative cubic Hénon maps-
Chaos 28(4), 1--15, 2018. PDF
V. Gelfreich and A. Vieiro. Interpolating vector fields for near identity maps and averaging.
Nonlinearity 31(9), 4263--4289, 2018. PDF Preprint ArXiv
T. Alarcón, D.Sánchez-Taltavull and A. Vieiro. Stochastic modelling of the eradication of the HIV-1 infection by stimulation of latently infected cells in patients under highly active anti-retroviral therapy.
Journal of Mathematical Biology, 2016 PDF PDF (SharedIT)
N.Míguel-Baños, C.Simó and A.Vieiro. Effect of Islands in Diffusive Properties of the Standard Map for Large Parameter Values.
Foundations of Computational Mathematics, vol. 15(1): 89--123, 2015. PDF
E.Fontich, C.Simó and A.Vieiro. The discrete Hamiltonian-Hopf bifurcation for 4D symplectic maps.
In Extended Abstracts Spring 2014, Hamiltonian Systems and Celestial Mechanics; Virus Dynamics and Evolution (Part I). Springer International Publishing, series Trends in Mathematics, vol. 4, pp. 77-81, 2015. ISBN 978-3-319-22128-1.
N.Míguel-Baños, C.Simó and A.Vieiro. From the Hénon conservative map to the Chirikov standard map for large parameter values.
Regular and Chaotic Dynamics 18(5): 469--489, 2013. PDF
C.Simó and A.Vieiro. A Physical Dissipative System with a Poincaré Homoclinic Figure-eight.
In Progress and challenges in dynamical systems. Springer Proceedings in Mathematics and Statistics, vol. 54, 383--394, 2013.
Ibáñez, S.; Pérez del Río, J.S.; Pumariño, A.; Rodríguez, J.Á (Eds.).
ISBN 978-3-642-38829-3.
S.Gonchenko, C.Simó and A.Vieiro. Richness of dynamics and global bifurcations in systems with a homoclinic figure-eight.
Nonlinearity 26(3): 621--679, 2013. PDF
For high resolution plots see the preliminary version: PS preprint
V.Gelfreich, C.Simó and A.Vieiro. Dynamics of 4D symplectic maps near a double resonance.
Physica D, 243(1): 92--110, 2013. PDF
C.Simó and A.Vieiro. Some remarks on the abundance of stable periodic orbits inside homoclinic lobes.
Physica D, 240(24): 1936--1953, 2011. PDF
C.Simó and A.Vieiro. Dynamics in chaotic zones of area preserving maps: close to separatrix and global instability zones.
Physica D, 240(8): 732--753, 2011. PDF
C.Simó and A.Vieiro. Planar Radial Weakly-Dissipative Diffeomorphisms.
Chaos 20(4): 1--18, 2010 (043138). PDF
E.M. Alessi, A. Farrés, A. Jorba, C. Simó and A. Vieiro. Efficient Usage of Self Validated Integrators for Space Applications.
European Space Agency, the Advanced Concepts Team, ESA Report. PDF
E.M. Alessi, A. Farrés, A. Jorba, C. Simó and A. Vieiro. Jet transport and applications to NEO's.
Proceedings of 1st IAA Planetary Defense Conference. ESA Conference Bureau, Granada (Spain), 2009. PDF
C.Simó and A.Vieiro. Resonant zones, inner and outer splittings in generic and low order resonances of area preserving maps.
Nonlinearity 22(5):1191--1246, 2009. PDF
C.Simó and A.Vieiro. A numerical exploration of weakly dissipative two-dimensional maps.
Proceedings of ENOC'05 (Eindhoven). PDF

Conferences

Past contributions

Any 2026

A. Vieiro. Discrete averaging for discrete maps.
RADS, Oviedo, June 3th 2026 slides

Any 2025

A. Vieiro. Dynamics of Near-identity Maps and Interpolating Vector Fields.
Dynamics Days Europe 2025, Thessaloniki, June 22th 2025
A. Murillo and A. Vieiro. Dynamics of 3D conservative maps near a normally elliptic invariant curve.
Dynamics Days Europe 2025, Thessaloniki, June 22th 2025
A. Vieiro. Dynamics of Near-identity Maps and Interpolating Vector Fields
SIAM DS25, Denver, May 11th, 2025. slides
A. Murillo and A. Vieiro. Periodic Forcing of a 3D Conservative Flow with an Invariant 2-sphere of Heteroclinic Connections to Saddle-foci.
SIAM DS25, Denver, May 11th, 2025.

Any 2024

A. Vieiro. Exploring chaos of near-identity maps through interpolating vector fields.
ICDEA 2024, París, June 25th, 2024.
A. Murillo and A. Vieiro. Periodic forcing of a 3D volume-preserving flow with a bubble of stability.
ICDEA 2024, París, June 25th, 2024.

Any 2023

A. Vieiro. Dinàmica d'aplicacions simplèctiques quasi-integrables.
6a Jornada de Sistemes Dinàmics de Catalunya. Octubre 11th, 2023. slides
A. Murillo and A. Vieiro. The splitting of the 2D invariant manifolds along a heteroclinic orbit to saddle-foci for a 3D time-periodic volume-preserving flow.
Nonlinear Dynamics: Theory and Applications - Conference named after L.P. Shilnikov. Nizhny Novgorod, May 11th, 2023. slides

Any 2022

E. Fontich and A. Vieiro. Exploring the dynamics after the transition to complex-saddle.
International Conference ``Dynamical Systems. Theory and Applications'', Nizhny Novgorod, June 28th, 2022. slides
A. Vieiro. Exploring diffusion in 4D near-the-Id symplectic maps.
Workshop TraX 2022, Barcelona, Spain, 11-12th May, 2022. slides

Any 2021

A. Vieiro. Escape times across a golden Cantorus and the evolution of approximant islands.
Annual International Conference on Dynamical Systems Shilnikov Workshop. Nizhny Novgorod, Rusia, 17th December, 2021. slides

Any 2019

E. Fontich, C. Simó and A. Vieiro. Hamiltonian-Hopf bifurcation under a periodic forcing. Quasi-periodicity in splitting of separatrices.
Lorentz Center workshop on Symplectic Dynamics. Leiden (Netherlands), 12nd April, 2019. poster

Any 2018

E. Fontich, C. Simó and A. Vieiro. Splitting of the separatrices after a Hamiltonian-Hopf bifurcation under periodic forcing.
Perspectives in Hamiltonian Dynamics. Venice (Italy), 21st June, 2018. slides
J.C. Tatjer and A. Vieiro. The dynamics of the QR flow.
Interdisciplinary Workshop on Multiple Scale Systems, Systems with Hysteresis and Trends in Dynamical Systems, MUPHYS-HSFS2018, CRM, Bellaterra (Barcelona, Spain), 28 May - 01 June, 2018. slides

Any 2017

J.C. Tatjer and A. Vieiro. The dynamics of the QR flow.
Dynamics, Bifurcations and Strange Attractors, Niznhy Novgorod, July 7th, 2017.
A. Vieiro (based on works with V. Gelfreich and C. Simó). Double resonances in 4D symplectic maps and diffusive properties.
XXV Congreso de ecuaciones diferenciales y aplicaciones (Cedya), Cartagena (Spain), 26-30 June, 2017.
N.Miguel-Baños, C. Simó and A. Vieiro. Anomalous diffusion in 2D and 3D volume-preserving map.
SIAM conference on Applications of Dynamical Systems, Snowbird (Utah,USA), 21-26 May, 2017.
E. Fontich, C. Simó and A. Vieiro. The splitting of separatrices associated to a Hamiltonian-Hopf bifurcation under the effect of a periodic forcing
5th Bremen Winter School and Symposium on Dynamical Systems and Fluids, Bremen, Germany, 27-31 March, 2017.

Any 2016

E. Fontich, C. Simó and A. Vieiro. Splitting of separatrices at a periodically forced Hamiltonian-Hopf bifurcation.
Dynamics, Bifurcations and Strange Attractors, Nizhny Novgorod 18-22 July, 2016. slides
E. Fontich, C. Simó and A. Vieiro. Periodically perturbed Hamiltonian-Hopf.
AIMS Conference on Dynamical Systems, Differential Equations and Applications, Orlando, Florida, 1-5 July, 2016.
V. Gelfreich and A. Vieiro. Geometry of double resonances of 4D symplectic maps and diffusive properties.
Dynamical Systems Workshop, Warwick, 6-8 June, 2016. slides

Any 2015

C. Simó, E. Fontich and A.Vieiro. La bifurcación Hamiltonian-Hopf de 2 grados de libertad bajo el efecto de un forzamiento periódico.
Congreso de jovenes investigadores RSME, Murcia, 10 Septiembre, 2015.
C. Simó, E. Fontich and A.Vieiro. Periodic forcing of a 2-dof Hamiltonian undergoing a Hamiltonian-Hopf bifurcation.
Dynamics, Bifurcations and Chaos 2015, Nizhny Novgorod (Rusia), on 20-24 July, 2015. slides

Any 2014

C. Simó, E. Fontich and A. Vieiro. The transition to complex-saddle in a Froeschlé-type map.
The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Madrid, Spain, on July 07-11, 2014. slides
C. Simó, E. Fontich and A. Vieiro. The discrete Hamiltonian-Hopf bifurcation for 4D symplectic maps , Conference on Hamiltonian systems and Celestial Mechanics (HAMSYS2014)
Barcelona, Spain, on June 02-06, 2014. slides

Any 2013

C. Simó and A.Vieiro. Study of an electro-mechanical device with figure-eight homoclinics in a domain with dissipation.
Dynamics Bifurcations and Strange Attractors (dedicated to the memory of Professor Leonid Pavlovich Shilnikov).
Nizhny Novgorod State University, Russia, on July 1-5, 2013. slides
S. Goncheko, C. Simó and A. Vieiro. A global study of 2D dissipative diffeomorphisms with a Poincaré homoclinic figure-eight.
SIAM conference on Applications of Dynamical Systems, Snowbird (Utah,USA), 23 May, 2013.
V. Gelfreich, C. Simó and A. Vieiro. Dynamics of 4d symplectic maps near a doubly resonant point.
4th one day meeting on dynamical systems, Centre for Applied Mathematics and Economics (CEMAPRE), Lisbon, May 2nd, 2013.
S. Goncheko, C. Simó and A. Vieiro. Dynamics of systems with a homoclinic figure-eight
Seminário de Sistemas Dinâmicos. Centro de Matemática e Aplicações Fundamentais (CMAF), Lisbon, May 3rd, 2013.

Any 2012

V. Gelfreich, C. Simó and A. Vieiro. Dynamics of 4d symplectic maps near a double resonance
DyToComp 2012, Bedlewo, Jun 30. slides
S. Goncheko, C. Simó and A. Vieiro. A global study of 2D dissipative diffeomorphisms with a Poincaré homoclinic figure-eight.
DS100P 2012, Gijón, September 3--7, 2012 slides
S. Goncheko, C. Simó and A. Vieiro. A global study of 2D dissipative diffeomorphisms with a Poincaré homoclinic figure-eight.
DDAYS 2012, Benicàssim, October 24--26, 2012.

Any 2011

C. Simó and A. Vieiro. Abundance of stable periodic orbits inside homoclinic lobes
Conference on Computational Methods in Dynamics, Trieste, 5 July, 2011 slides
C. Simó and A. Vieiro. Dynamics in chaotic zones (APMs): inner/outer splittings of separatrices
Workshop on instabilities in Hamiltonian systems, Toronto, 15 June, 2011 slides
C. Simó and A. Vieiro. Resonant chaotic zones: dynamical consequences of the difference between the inner/outer splittings of separatrices
Equadiff 2011, Loughborough, 1 August, 2011 slides
C. Simó and A. Vieiro. Abundància d'òrbites periòdiques estables dins dels lòbuls homoclínics
Trobada de Joves Investigadors de la Societat Catalana de Matemàtiques, Barcelona, 14 d'octubre de 2011 slides

Any 2010

A. Vieiro. Quantitative description of the dynamics in resonant islands
EU Young and Mobile Workshop: Dynamical Systems and Number Theory, Edinburgh 17-19 May, 2010 slides
C. Simó and A. Vieiro. Dynamics in chaotic zones of area preserving maps (APMs): close to separatrix and global instability zones
8th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, Dresden, 24--28 May, 2010 slides
A. Vieiro. Study of the effect of conservative and weakly dissipative perturbations on symplectic maps and Hamiltonian systems
Ddays 2010 (Calatayud) slides
A. Vieiro. Quantitative description of the dynamics in resonant islands
I ENJIM, Seville 1--3 Setember 2010 slides

Any 2009

C. Simó and A. Vieiro. Some quantitative global aspects of (perturbations of) area preserving maps
International Workshop on ``Hamiltonian Approaches of ITER Physics'', CIRM, Marseille, France 2-6 November 2009 slides

Any 2008

C. Simó and A. Vieiro. Quantitative global phase space analysis of APM
Workshop on Stability and Instability in Mechanical Systems: Applications and Numerical Tools. slides
C. Simó and A. Vieiro. Métodos intervalares de integración validada: aplicaciones a la mecánica celeste
Workshop on Stability and Instability in Mechanical Systems: Applications and Numerical Tools. slides
E.M.Alessi; A. Farrés; A. Jorba and A.Vieiro. Course: Numerical Integration Methods Applied to Astrodynamics and Astronomy (IV)
1st Astronet Trainning School, Barcelona, Septembre 15 -- 19 2008. slides

Any 2005

C. Simó and A. Vieiro. First Steps in the Study of Weakly Dissipative Two-Dimensional Maps
NSDS'05, Seville 2005 slides
C. Simó and A. Vieiro. A Numerical Exploration of Weakly Dissipative Two-Dimensional Maps
ENOC'05, Eindhoven 2005 slides

Outreach

Article de premsa. Selected by Atomium Culture.
E.M. Alessi, A. Farré, A. Jorba, C. Simó and A.Vieiro. The hammer of God
Published in The Irish Times (07/08/2011). The hammer of God
També es pot trobar a: Gottes Hammer
Juliols UB 2012: Transbord a la ISS: guia bàsica per viatjar per l'espai
Xerrada-Taller UB 2012: Com i perquè es pot viatjar per l'espai
Ecuaciones de Lorenz: Derivación de las ecuaciones de Lorenz Bifurcaciones en el sistema de Lorenz

Useful links

Web de la Facultat de Matemàtiques i Informàtica (UB): mat
Web de la Universitat de Barcelona: UB
Web del grup de sistemes dinamics UB: UB Dynamical Systems Group
MathScinet: mathscinet
Campus virtual UB: campusvirtual
Biblioteca UB: Biblioteca UB - Cercabib UB
Intranet UB: intranetUB
OVT: OVT
RSME: rsme
SCM: scm
ICMAT: icmat
CRM: crm

Miscellaneous

La órbita del telescopio James Webb y el problema de los tres cuerpos (by À. Jorba, El País, Café y Teoremas, Oct 03, 2022)

Teaching Mathematics by Arnold.

El vestit nou del pseudopedagog modern. Prof. J. Aulet (Diari Núvol)

Carta als meus estudiants de filosofia (i a tots aquells a qui els avergonyeix continuar obeint). M. Garcés (Diari Núvol, inclosa a ``Escola d'aprenents'', Galaxia Gutenberg, 2020)