At Drexel
bob [at] newton.physics.drexel.edu
Dr. Gilmore is director of the Nonlinear Dynamics Group at
Drexel University. A common theme throughout his work is the
desire to bring modern mathematics into physics. A first
incarnation of this goal was his detailed study of Lie groups
and their applications for Physics (see the book
page for his Lie Groups text publication). Dr. Gilmore next
turned to the subject of Catastrophe Theory (again, see the book
page for this text). The text that resulted was translated into
Russian on the recommendation of V. I. Arnol'd. This work would
lay the foundation for Dr. Gilmore's entry into Nonlinear
Dynamics where he, his colleagues, and his students would create
a suite of topological tools for the analysis of nonlinear data.
His long-range goal is to develop an analysis procedure for
nonlinear data beyond its current three dimensional limit.
arunasri [at] newton.physics.drexel.edu
Ms. Nishtala has worked on the so called "Arnold's tongue",
in order to understand the orbit-orbit mode locking behavior in
the Solar System. She is currently studying the topology of
dynamical systems at the internal embedding level. This project
is focused to braid non-linear systems in such a way that the
relative rotation rates and linking numbers of a pair of orbits
can be recognized and the genus dependent topology of any system
completely understood. She is also working on trying to produce
subharmonic strange attractors.
Nicola Romanazzi
nr44 [at] drexel.edu
Mr. Romanazzi is in his third year of graduate studies under
the advisement of Dr. Gilmore. He has previously studied the
characterization of inequivalant templates of strange attractors
in R^3. He is currently studying the effect of embeddings,
showing that the stretch and fold mechanism is an invarient of
embeddings. Mr. Romanazzi plans to do his thesis work on time
serious and embeddings, with an eye towards their applications
for empirical data.
d.j.cross [at] drexel.edu
Mr. Cross is in the fifth year of his graduate studies
under the advisement of Dr. Gilmore. His research interests are
in mathematical physics, Field Theory, Mach's Principle, and
higher dimensional nonlinear dynamics. He is currently using insights
in Nonlinear Dynamics to investigate the magnetic field lines of closed
knotted wires.
timjones [at] physics.drexel.edu
Mr. Jones is in his fifth
year of graduate studies. His
previous research resulted in second authorship on an Astrophysical
Journal paper with Drs. Goldberg, Hoyle, Vogeley et al.
He did his Oral Qualifier on Quantum Decoherence with a
committee that included Dr. Lorenzo Narducci.
Currently taking courses in advanced mathematics to
augment his current Nonlinear Dynamics research project with
Dr. Gilmore, Mr. Jones is eagerly awaiting to begin his
thesis.
Benjamin Coy
btc24 [at] drexel.edu
Mr. Coy is in his third year of graduate studies and is
advised by Dr. Gilmore. Ben has done previous research in the
nonlinear dynamics field with a project investigating the
calculation of local Lyapunov exponents. He is currently
studying strange attractors generated by nonlinear
oscillators.
Ryan Michaluk
rmm622 [at] drexel.edu
Mr. Michaluk is in his second year of graduate studies under
Dr. Robert Gilmore. Mr. Michaluk has previously researched
harmonic knot embeddings and other techniques for analyzing time
series. Ryan enjoys strange attractors and long walks on the
beach.
Elsewhere
ramos [at] newton.physics.drexel.edu
Mr. Ramos recently received his PhD under Dr. Gilmore. His has worked in quantization of constrained systems such as free electromagnetic fields and Dirac fields. His PhD work was on a Lagrangian Formalism of Gravitoelectromagnetism including new guage transformations.
tsankov [at] newton.physics.drexel.edu
Dr. Gilmore and Dr. Tsankov continue to collaborate in the search for new topological methods to classify higher dimensional chaotic systems. Dr. Tsankov is also interested in applications of Differential Geometry and Topology to problems in Classical and Celestial Mechanics, Biomechanics, and Control Theory.
Prof. Lefranc carries out both experimental and theoretical work. He has developed an extensive data base from a series of laser experiments. Chaotic data sets have been developed on periodically driven lasers. These data sets contain attractors of three dimensions and higher. He has also developed a suite of powerful tools for extracting unstable periodic orbits from data, assigning a symbolic name to these orbits, and computing their topological entropy in a simple, straightforward way. He and Prof. Gilmore are together attempting to extend topological analysis methods into higher dimensions. Together he has written a book with Prof. Gilmore: R. Gilmore and M. Lefranc, The Topology of Chaos, NY: Wiley, 2002.
Prof. Letellier has an interest in determining the mechanisms that contribute to the generation of distinct types of chaotic attractors. He is also interested in the effects of symmetry on strange attractors. Prof. Letellier has used symmetry to generate a large number of strange attractors with different global topological structures. Together with Prof. Gilmore, he is completing a text: R. Gilmore and C. Letellier, The Symmetry of Chaos, (nearing completion).
gb27 [at] drexel.edu
Mr. Byrne is a 2004 graduate from Drexel University where he received his B.S. in Physics. As an undergraduate, he collaborated with Dr. Gilmore and Dr. Letellier in an NSF sponsored project investigating the global relationships between cover (symmetric) and image (non-symmetric) chaotic strange attractors. Under Dr. Gilmore's supervision, Mr. Byrne completed his undergraduate thesis "First Return Maps and Bounding Tori as Tools for Topological Analysis of Chaotic Data". The project developed a procedure which facilitates the application of topological methods of analysis to noisy experimental data. His current research focuses on understanding how the basic mechanisms responsible for chaotic behavior in strange attractors change under symmetry transformation and control parameter variation.