About me

Contact

Postal address:

Department of Mathematics
University of Maryland
Mathematics Building,
College Park, MD 20742-4015 USA

Phone:

(+1) 301 405 5132

E-mail:

marcel dot guardia at upc dot edu, mguardia at umd dot edu.

Research Interests

Hamiltonian Systems, Arnol'd diffusion, Exponentially small phenomena, Hamiltonian Partial Differential Equations, Celestial Mechanics. Here is my CV.

 

 

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Research

Preprints

• Marcel Guàrdia, Vadim Kaloshin
  Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation
  76 pages. See the article on the arXiv.
• Jacques Féjoz, Marcel Guàrdia, Vadim Kaloshin, Pablo Roldan
  Diffusion along mean motion resonance in the restricted planar three-body problem
  68 pages. See the article on the arXiv.
• Inma Baldomá, Marcel Guàrdia, Ernest Fontich, Tere M. Seara
  Exponentially small splitting of separatrices beyond Melnikov analysis: rigorous results
  117 pages. See the article on the arXiv.

Publications

• Marcel Guàrdia
  Splitting of separatrices in the resonances of nearly integrable Hamiltonian Systems of one and a half degrees of freedom
  To appear in Discrete and Continuous Dynamical Systems A. Preprint version on the arXiv.
• Marcel Guàrdia, Tere M. Seara
  Exponentially and non-exponentially small splitting of separatrices for the pendulum with a fast meromorphic perturbation
  Nonlinearity, 24 (5): 1367-1412 (2012). [PDF].
• Marcel Guàrdia, Tere M. Seara, Marco Antonio Teixeria
  Generic bifurcations of low codimension of planar Filippov Systems
  Journal of Differential Equations, 250 (4): 1967-2023 (2011) . [PDF].
• Marcel Guàrdia, S. John Hogan, Tere M. Seara
  An analytical approach to codimension 2 sliding bifurcations in the dry friction oscillator
  SIAM Journal on Applied Dynamical Systems, 9: 769–798 (2010). [PDF].
• Marcel Guàrdia, Carme Olivé, Tere M. Seara
  Exponentially small splitting for the pendulum: a classical problem revisited
  Journal of Nonlinear Science, 20: 595-685, (2010) . [PDF].

Given Talks

Here you will find a selection of slides of presentations in seminars and congresses. Please note that these have not been revised and they may have misprints.

• Growth of Sobolev norms for the cubic defocusing nonlinear Schrodinger equation in polynomial time , Princeton University Analysis Seminar. April 9, 2012.
• An instability mechanism along the mean motion resonances in the restricted three body problem , Nanjing Conference on Hamiltonian Dynamics . Nanjing, China. August 21-28, 2011
• Exponentially small splitting of separatrices for one and a half degrees of freedom Hamiltonian Systems close to a resonance , McMaster University PDE/Analysis Seminar. April 15, 2011.
• Analytic properties of one and a half degrees of freedom Hamiltonian Systems and exponentially small splitting of separatrices , University of Maryland Dynamical Systems Seminar. November 18, 2010.
• Exponentially small splitting of separatrices for the pendulum with fast periodic or quasiperiodic meromorphic perturbation , Equadiff 11. Loughborough, United Kingdom. August 1-5, 2011.
• Exponentially small splitting of separatrices of the pendulum: two different examples , Universitat de Barcelona - Universitat Politècnica de Catalunya Dynamical Systems Seminar. July 8, 2009.
• Global phenomena in a neighborhood of codimension two local singularities of planar Filipov systems , International Workshop on Resonance Oscillations and Stability of Nonsmooth Systems. London, United Kingdom. June 16-25, 2009.

 

 

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Teaching

I'm not teaching this semester.

 

 

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Last update July 25, 2012.