Tere M-Seara

Professor, Icrea Academia

Departament de Matemàtiques. Universitat Politècnica de Catalunya (UPC)

• Contact information
• Publications
• Preprints
• Docència

Books

• Estudi de fenòmens homoclinics en sistemes propers a integrables.
  T. M. Seara
  Tesi doctoral. Pub. Ed. Univ. Barcelona. Barcelona, 1991.
  

• Cálcul Numéric
  C. Bonet, A. Jorba, T. M. Seara, J. Masdemont, M. Ollé, A. Susín, M. Valéncia
  CPDA, ETSEIB-UPC. ISBN 84-7653-097-8. Barcelona, 1991.
  

Papers

2020

• A general mechanism of instability in Hamiltonian systems: Skipping along a normally hyperbolic invariant manifold
  Marian Gidea, Rafael de la Llave, T. M-Seara.
  Discrete and continuous dynamical systems 2020.
  DOI: 10.3934/dcds.2020166 (pdf)
  

• Critical velocity in kink-defect interaction models: rigorous results
  Otávio M. L. Gomide, Marcel Guardia, Tere M-Seara.
  Journal of Differential Equations, 2020
  DOI: 10.1016/j.jde.2020.02.030 (pdf)
  

• Hopf-Zero singularities truly unfold chaos
  I. Baldomá, S. Ibañez, Tere M-Seara.
  Communications in Nonlinear Science and Numerical Simulation, 2020
  DOI: 10.1016/j.cnsns.2019.105162 (pdf)
  

• Phase-locked states in oscillating neural networks and their role in neural communication.
  A. Pérez-Cervera, T. M-Seara, G. Huguet.
  Communications in Nonlinear Science and Numerical Simulation, 80, 2020
  DOI: 10.1016/j.cnsns.2019.104992 (pdf)
  

2019

• A General Mechanism of Diffusion in Hamiltonian Systems: Qualitative Results.
  Marian Gidea, Rafael de la Llave, T. M-Seara.
  Communications on pure and applied mathematics, 73 (1): 110-149, 2019
  DOI: 10.1002/cpa.21856 (pdf)
  

• The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability.
  A. Pérez-Cervera, P. Ashwin, G. Huguet, T. M-Seara, J. Rankin.
  The Journal of Mathematical Neuroscience 9, article number: 7 (33pp), 2019
  DOI:10.1186/s13408-019-0075-2 (pdf)
  

• A Geometric Approach to Phase Response Curves and Its Numerical Computation Through the Parameterization Method.
  A. Pérez-Cervera, T. M-Seara, G. Huguet.
  Journal of Nonlinear Sience 29(6): 2877-2910, 2019
  DOI:10.1007/s00332-019-09561-4 (pdf)
  

2018

• Global Instability in the Restricted Planar Elliptic Three Body Problem.
  A. Deslhams, V. Kaloshin, A. de la Rosa, T. M-Seara.
  Communications in Mathematical Physics 366(3):1173-1228, 2019
  DOI:10.1007/s00220-018-3248-z (pdf)
  

• Breakdown of a 2D Heteroclinic Connection in the Hopf-Zero Singularity (I).
  I. Baldomá, O. Castejón, T. M. Seara.
  Journal of Nonlinear Science 28(5): 1551-1627, 2018.
  DOI:https://doi.org/10.1007/s00332-018-9458-x (pdf)
  

• Breakdown of a 2D Heteroclinic Connection in the Hopf-Zero Singularity (II).
  I. Baldomá, O. Castejón, T. M. Seara.
  Journal of Nonlinear Science 28(4): 1489-1549, 2018.
  DOI:https://doi.org/10.1007/s00332-018-9459-9 (pdf)
  

• A Regularization around a generic codimension one fold-fold singularity.
  C. Bonet Revés,J. Larrosa, T. M. Seara.
  Journal of Differential Equations 265: 1761-1838, 2018.
  DOI: https://doi.org/10.1016/j.jde.2018.04.047 (pdf)
  

2017

• A unified approach to explain contrary effects of hysteresis and smoothing in nonsmooth systems.
  C. Bonet, E. Fossas, M. R. Jeffrey, T. M. Seara.
  Commun Nonlinear Sci Numer Simulat 50: 142–168, 2017.
  DOI:http://doi.org/10.1016/j.cnsns.2017.02.014 (pdf)
  

• Stability of the phase motion in race-track microtrons.
  Yu.A. Kubyshin a, O. Larreal b, R. Ramírez-Ros, T. M. Seara.
  Physica D 349: 12-26, 2017.
  DOI: http://doi.org/10.1016/j.physd.2017.03.001 (pdf)
  

• Oscillatory orbits in the restricted elliptic planar three body problem.
  M. Guárdia, P. Martín, L. Sabbagh, T. M. Seara.
  Discrete and Continuous Dynamical Systems 37 (1): 229-256, 2017.
  DOI: http://dx.doi.org/10.3934/dcds.2017009, 2016. (pdf)
  

• On the asymptotic wavenumber of spiral waves in $λ-ω$ systems.
  M. Aguareles, I. Baldomá, T.M. Seara.
  Nonlinearity 30 (1): 90-114, 2017.
  doi: https://doi.org/10.1088/1361-6544/30/1/90 (pdf)
  

2016

• Regularization of sliding global bifurcations derived from the local fold singularity of Filippov systems.
  C. Bonet-Revés, T.M. Seara.
  Discrete and continuous dynamical systems 36(7), 3545-3601, 2016.
  doi:10.3934/dcds.2016.36.3545 , 2016. (pdf)
  

• Instability of high dimensional Hamiltonian Systems: Multiple resonances do not impede diffusion.
  A. Delshams, R. de la Llave, T.M. Seara.
  Adv. Math. 294, 689-755, 2016.
  doi:10.1016/j.aim.2015.11.010 , 2016. (pdf)
  

• Oscillatory motions for the restricted planar circular three body problem.
  M. Guárdia, P. Martín, T. M. Seara.
  Inventiones Mathematicae. 203, 417-492, 2016.
  DOI: 10.1007/s00222-015-0591-y, 2015. (pdf)
  

2014

• The scattering map in two coupled piecewise-smooth systems, with numerical application to rocking blocks
  A. Granados, S.J. Hogan, T.M. Seara.
  Physica D: Nonlinear Phenomena, 269, 1-20, 2014. (pdf)
  

2013

• Exponentially Small Heteroclinic Breakdown in the Generic Hopf-Zero Singularity.
  I. Baldomá, O. Castejón, T. M. Seara
  Journal of Dynamics and Differential equations. 25(2), 335--392, 2013. (pdf)
  

2012

• Exponentially small splitting of separatrices beyond Melnikov analysis: rigorous results
  Baldomá, E. Fontich, M. Guárdia, T. M. Seara.
  Journal of Differential equations 253, 3304-3439, 2012. (pdf)
  

• The Melnikov method and subharmonic orbits in a piecewise smooth system
  A. Granados, S.J. Hogan, T.M. Seara
  SIAM J. Applied Dynamical Systems 11(3): 801-830, 2012. (pdf)

• Exponentially and non-exponentially small splitting of separatrices for the pendulum with a fast meromorphic perturbation
  M. Guárdia, T. M. Seara
  Nonlinearity, 25: 1367-1412, 2012. (pdf)

2011

• Exponentially small splitting of separatrices in the perturbed McMillan map
  P. Martín, D. Sauzin, T. M. Seara
  Discrete and continuous dynamical systems 31(2): 301-371, 2011. (pdf)
  

• Resurgence of inner solutions for perturbations of the McMillan map
  P. Martín, D. Sauzin, T. M. Seara
  Discrete and continuous dynamical systems 31(1): 165-207, 2011. (pdf)
  

• Periodic solutions with nonconstant sign in Abel equations of the second kind
  J. M. Olm, X. Ros-Oton, T. M. Seara
  Journal of mathematical analysis and applications 381(2): 582-589, 2011. (pdf)
  

• Generic bifurcations of low codimension of planar Filippov Systems
  M. Guardia, T. M. Seara. M. A. Teixeira
  Journal of Differential equations 250: 1967-2023, 2011. (pdf)
  

2010

• Exponentially small splitting for the pendulum: a classical problem revisited
  M. Guardia, C. Olive, T. M. Seara
  Journal of Nonlinear Science 20(5): 595-685, 2010. (pdf)
  

• An analytical approach to codimension-2 sliding bifurcations in the dry friction oscillator
  M. Guardia, S.J. Hogan, T. M. Seara
  SIAM J. Applied Dynamical Systems 9(3): 769-798, 2010. (pdf)
  

2009

• Two-parameter bifurcation curves in power electronic converters
  E. Fossas, S. J. Hogan, T~.M. Seara
  International Journal Of Bifurcation And Chaos In Applied Sciences And Engineering 19(1): 349-357, 2009. (pdf)
  

• Numerical Computation of the Asymptotic Size of the Rotation Domain for the Arnold Family
  T. M. Seara, J. Villanueva
  Physica D 238: 197-208, 2009. (pdf)
  

2008

• The inner equation for generic analytic unfoldings of the Hopf-zero singularity
  I. Baldomá, T. M.Seara
  Discrete and Continuous Dynamical Systems-Series B 10(2-3): 323-347, 2008. (pdf)
  

• Bounding the Output Error in a Buck Power Converter Using Perturbation Theory
  F. Angulo, E. Fossas, T.M. Seara, G. Olivar
  Mathematical Problems in Engineering. ID 732039: 1-20, 2008 (pdf)
  

• Geometric approaches to the problem of instability in Hamiltonian systems. An informal presentation
  A. Delshams, M. Gidea, R. de la Llave, T.M. Seara
  Hamiltonian Dynamical Systems and Applications, NATO Sci. Peace Secur. Ser. B Phys. Biophys 24: 285-336, 2008. Springer, Dordrecht. . (pdf)
  

• Geometric properties of the scattering map of a normally hyperbolic invariant manifold
  A. Delshams, R. de la Llave, T.M. Seara
  Adv. Math. 217(3): 1096-1153, 2008. (pdf)
  

2006

• Breakdown of heteroclinic orbits for some analytic unfoldings of the Hopf-zero singularity.
  I. Baldomá, T. M.Seara
  Journal of Nonlinear Science 16:6: 543-582, 2006. (pdf)
  

• On the numerical computation of Diophantine rotation numbers of analytic circle maps.
  T. M.Seara, Jordi Villanueva
  Physica D: Nonlinear Phenomena 217:2: 107-120, 2006. (pdf)
  

• Orbits of unbounded energy in quasi-periodic perturbations of geodesic flows
  A. Delshams, R. de la Llave, T.M. Seara
  Adv. Math. 202(1): 64-188, 2006. (pdf)
  

• A Geometric Mechanism for Diffusion in Hamiltonian Systems Overcoming the large Gap Problem: Heuristics and Rigorous Verification on a Model
  A. Delshams, R. de la Llave, T.M. Seara
  Mem. Amer. Math. Soc. 179(844): 1-141, 2006. (pdf)
  

2005

• Two examples of resurgence.
  C. Olivée, D. Sauzin, T.M. Seara
  Contemporary Mathematics 373: 355-371, 2005. (pdf)
  

2004

• Exponentially small splitting for whiskered tori in Hamiltonian Systems: Flow-box coordinates and upper bounds.
  A. Delshams, Pere Gutiérrez y T.M.~Seara
  Discrete and Continuous Dynamical Systems 11(4): 785-826, 2004. (pdf)
  

• Asymptotic Size of Herman Rings of the Complex Standard Family by Quantitative Quasiconformal Surgery.
  N. Fagella, T. M. Seara i Jordi Villanueva
  Ergodic Theory and Dynamical Systems 24(3): 735-766, 2004. (pdf)
  

2003

• Resumació de Borel i teoria de la ressurgència.
  D. Sauzin, T.M. Seara
  Butlletí de la Societat Catalana de Matemàtiques 18(1): 131-153, 2003. (pdf)
  

• A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: Announcement of results.
  A. Delshams, R. de la Llave y T.M. Seara
  ERA Amer. Math. Soc 9: 125-134, 2003. (pdf)
  

• Resurgence in a Hamilton-Jacobi Equation.
  C. Olivée, D. Sauzin, T.M. Seara
  Annales de l'Institute Fourier 53: 1185-1235, 2003. (pdf)
  

2000

• Asymptotic Behaviour of the Domain of Analyticity of Invariant Curves of the Standard Map.
  T. M. Seara, J. Villanueva
  Nonlinearity, 13: 1699-1744, 2000. (pdf)
  

• A geometric approach to the existence of orbits with unbounded energy in generic periodic perturbations by a potential of generic geodesic flows of T2.
  A. Delshams, R. de la Llave, T. M. Seara
  Comm. Math. Phys., 209 (2): 353-392, 2000. (pdf)
  

1998

• Adiabatic Invariant of the Harmonic Oscillator, Complex Matching and Resurgence.
  C. Bonet, D. Sauzin, T. M. Seara, M. València
  SIAM J. Math. An., 29 (6): 1335-1360, 1998. (pdf)
  

1997

• Lower and upper bounds for the splitting of separatrices of the pendulum under a fast quasiperiodic forcing.
  A. Delshams, V.G. Gelfreich, A. Jorba, T. M. Seara.
  Electron. Res. Announc. Amer. Math. Soc., 3: 1-10, 1997. (pdf)
  

• Exponentially small splitting of separatrices under fast quasiperiodic forcing.
  A. Delshams, V.G. Gelfreich, A. Jorba, T. M. Seara.
  Comm. Math. Phys., 189 (1): 35-71, 1997. (pdf)
  

• Splitting of separatrices in Hamiltonian systems with one and a half degrees of freedom.
  A. Delshams, T. M. Seara.
  Math. Phys. Electron. J., 3 (1): 1-40, 1997. (pdf)
  

1992

• An asymptotic expression for the splitting of separatrices of the rapidly forced pendulum.
  A. Delshams, T. M. Seara.
  Commun. Math. Phys., 150: 433-463, 1992. (pdf)
  

Proceedings

• Exponentially Small Expressions for Separatrix Splittings
  A. Deslhams, T.M.Seara
  Abstract
  Seminar on Dynamical Systems
  

Last update January 2020.

Some links

• UPC DS-group
• JISD 2020 (18TH School of interactions between Dynamical Systems and Partial Diferential Equations)
• UB-UPC DS-group
• UAB DS-group
• DANCE (Spanish DS net)
• Arxiv

Others

• FME (UPC)
• ETSEIB (UPC)

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