**Mark Edelman’s Statement of Research Interests **

In 1982 at the department of
Astrophysics of the

from MIT and published in “The Astrophysical Journal” in
1986. Bertschinger’s article was cited almost one hundred times. My publication
gave me an opportunity to communicate with astrophysicists from Pulkovo
observatory and Ioffe Physico-Technical Institute.

The next natural step was to
consider the corrugation instability of magnetized radiative and adiabatic
shocks, as the astrophysical plasma, especially for the case of the accretion
onto magnetized stars, is always magnetized. As the result, the whole linear
theory of corrugation instability of radiative and magnetized gases was
created. I ended my work on this theory in 1995 with the work done in
collaboration with James Stone from

In 1995 George Zaslavsky
offered me to work on the computer simulations related to chaos theory at the
Courant Institute. I accepted this offer and since 1995 the chaos theory has
been the subject of my research. Particular areas of my interest include
research on the connection between topological properties of phase space of
dynamical systems and transport coefficients, pseudochaos (with zero Lyapunov exponent), description of dynamical systems by fractional
differential equations and numerical solution of such equations. Design of
corresponding software (visual C++) and web design are just hobbies. An
application Phase Portrait Builder can be sent upon request and I can issue a
password for my educational site: http://cims.nyu.edu/~edelman/MyCourse/Precalculus0/Precalculus/

In their pioneering work Nick
Laskin and George Zaslavsky (Physica A, 2006) showed that systems of long range
interacting oscillators in the infrared limit (small *k*) can be adequately described by fractional partial differential
equations. This work stimulated activities in our group related to
generalization of the properties of well known PDEs like sine-Gordon equation,
non-linear Shrödinger equation, Ginzburg-Landau equation etc. for the case of
fractional space derivatives. This is also the area of my main interest at the
present time.