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
2023
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Traveling waves in a model for cortical spreading depolarization with slow-fast dynamics.
D. Reyner-Parra, C. Bonet, T. M-Seara, G. Huguet
Chaos. An Interdisciplinary Journal of Nonlinear Science 33 (8), 2023
DOI: 10.1063/5.0160509 (pdf)
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Arnold diffusion in a model of dissipative system.
S. W. Akingbade, M. Gidea, T. M-Seara
Siam Journal on Applied Dynamical Systems 22 (3), 2023
DOI: 10.1137/22M1525508 (pdf)
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Breakdown of Heteroclinic Connections in the Analytic Hopf-Zero Singularity: Rigorous Computation of the Stokes Constant.
I. Baldomá, M. Capiński, M. Guardia, T. M-Seara
Journal of Nonlinear Science 33 (28), 2023
DOI: 10.1007/s00332-022-09882-x (pdf)
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Generalised analytical results on n-ejection-collision orbits in the RTBP. Analysis of bifurcations.
T. M-Seara, M. Ollé, O. Rodriguez, J. Soler
Journal of Nonlinear Science 33 (17), 2023
DOI: 10.1007/s00332-022-09873-y (pdf)
2022
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Two regularizations of the grazing-sliding bifurcation giving non equivalent dynamics.
C. Bonet-Revés, T.M-Seara.
Journal of Differential Equations 332: 219-277, 2022
DOI: 10.1016/j.jde.2022.05.028 (pdf)
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Oscillatory motions and parabolic manifolds at infinity in the planar circular restricted three body problem.
M. Capiński, M. Guardia, P. Martín,T. M-Seara, P. Zgliczyński.
Journal of Differential Equations 320: 316- 370, 2022
DOI: 10.1016/j.jde.2022.02.056 (pdf)
2021
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Symbolic dynamics in the restricted elliptic isosceles three body problem.
M. Guardia, J. Paradela, T. M-Seara, C. Vidal.
Journal of Differential Equations 294 (5): 143-177, 2021
DOI: 10.1016/j.jde.2021.05.017 (pdf)
2020
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Oscillatory orbits in the restricted planar four body problem.
T. M-Seara, J. Zhang.
Nonlinearity 33 (12): 6985–7015, 2020
DOI: 10.1088/1361-6544/abaf5f (pdf)
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Global phase-amplitude description of oscillatory dynamics via the parameterization method.
A. Pérez-Cervera, T. M-Seara, G. Huguet.
Chaos 30(8), o83117:1-30, 2020
DOI: 10.1063/5.0010149 (pdf)
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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 40(12): 6795-6813, 2020.
DOI: 10.3934/dcds.2020166 (pdf)
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Critical velocity in kink-defect interaction models: rigorous results
Otávio M. L. Gomide, Marcel Guardia, Tere M-Seara.
Journal of Differential Equations 269(4):3282-3346, 2020
DOI: 10.1016/j.jde.2020.02.030 (pdf)
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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, 2020
DOI: 10.1002/cpa.21856 (pdf)
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Study of Periodic Orbits in Periodic Perturbations of Planar Reversible Filippov
Systems Having a Twofold Cycle
D. D. Novaes, T. M-Seara, M. A. Teixeira, I. O. Zeli.
SIAM Journal on Applied Dynamical Systems (SIADS) 12(2): 1343–1371, 2020
DOI: 10.1137/19M1289959 (pdf)
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Hopf-Zero singularities truly unfold chaos
I. Baldomá, S. Ibañez, Tere M-Seara.
Communications in Nonlinear Science and Numerical Simulation 84, 2020
DOI: 10.1016/j.cnsns.2019.105162 (pdf)
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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
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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)
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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)
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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
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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)
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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)
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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
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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)
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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)
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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)
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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
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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)
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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)
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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)
2015
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Regularization of non-smooth systems using analytic functions.
C. Bonet-Revés, T.M. Seara.
talk at SIAM conf. of Appl. Dyn. Systems.
Slides of the talk.(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
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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)
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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)
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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.
DOI:https://doi.org/10.1016/j.aim.2007.08.014 (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
DOI:https://doi.org/http://dx.doi.org/10.1090/memo/0844
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 February 2023.