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
2018
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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, 2018.
DOI:10.1007/s00220-018-3248-z (pdf)
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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)
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. Gu\`{a}rdia, 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. (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 June 2018.
