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Jean-Philippe
Lessard
Here is a link
to my webpage at Laval. |
Positions
- Université Laval,
Quebec City, Canada, (Assistant Professor), Aug. 2011 -
Present.
- Rutgers University,
Piscataway, USA (Postdoctoral Associate) Jan. 2008 -
May 2008; Jan. 2009 - Aug. 2009
Education
Publications
and Preprints
14)
Rigorous numerics in Floquet
theory: computing stable and unstable bundles of periodic orbits
Submitted,
2011. With Roberto Castelli.
13)
Efficient rigorous
numerics for high-dimensional PDEs via one-dimensional estimates
Submitted,
2011. With Marcio Gameiro.
12)
Computational fixed point
theory for differential delay equations with multiple time lags
Submitted,
2010. With Gábor Kiss.
Here is a
link
containing relevant files associated to this work.
11)
Rigorous numerics for
symmetric connecting orbits: even homoclinics of the Gray-Scott
equation
SIAM Journal on Mathematical
Analysis, 43 (4): 1557-1594, 2011. With J.B. van den
Berg, J.D. Mireles James and K. Mischaikow.
Here is a
link
containing relevant files associated to this work.
10)
Existence of secondary
bifurcations or isolas for PDEs
Nonlinear Analysis: Theory,
Methods and Applications, 74 (12): 4131-4137, 2011. With
Marcio Gameiro.
9)
Rigorous computation of smooth
branches of equilibria for the three-dimensional Cahn-Hilliard
equation
Numerische Mathematik, 117 (4): 753-778,
2011. With Marcio Gameiro.
8)
Analytic estimates and rigorous
continuation for equilibria of higher-dimensional PDEs
Journal of Differential Equations, 249 (9): 2237-2268, 2010. With
Marcio Gameiro.
7)
Global smooth solution curves
using rigorous branch following
Mathematics
of Computation, 79 (271), 1565-1584, 2010. With Jan Bouwe
van den Berg and Konstantin Mischaikow.
6)
Recent advances about the uniqueness
of the slowly oscillating periodic solutions of Wright's
equation
Journal of Differential Equations, 248 (5): 992-1016, 2010.
Here is a
link
containing relevant files associated to this work.
5)
Chaotic braided solutions via rigorous
numerics: chaos in the Swift-Hohenberg equation
SIAM Journal on Applied Dynamical Systems, 7
(3): 988-1031, 2008. With Jan Bouwe van den Berg.
4)
Validated continuation over
large parameter ranges for equilibria of PDEs
Mathematics and Computers in Simulation, 79 (4): 1368-1382, 2008.
With Marcio Gameiro and Konstantin Mischaikow.
3)
Validated continuation for
equilibria of PDEs
SIAM Journal on Numerical Analysis, 45(4):
1398-1424, 2007. With Sarah Day and Konstantin
Mischaikow.
2)
Validated continuation for infinite dimensional
problems
Ph.D. dissertation. Georgia Institute of
Technology, 2007.
1)
Bifurcations et chaos dans le système
de Lorenz
Master Thesis. Université de
Montréal, 2002.
Mathematical
Interests
- Dynamical Systems
(PDEs, ODEs & Delay Equations)
- Rigorous Numerical Techniques
- Algebraic Topology
& Topological Methods (Conley Index Theory,
Morse Theory & Floer Homology)
- Bifurcation Theory