Rajagopalan, S; Dr. Sabir, M(Cochin University Of Science And Technology, March 4, 2002)
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Abstract:
The study of simple chaotic maps for non-equilibrium processes in statistical
physics has been one of the central themes in the theory of chaotic dynamical
systems. Recently, many works have been carried out on deterministic diffusion
in spatially extended one-dimensional maps This can be related to real physical
systems such as Josephson junctions in the presence of microwave radiation and
parametrically driven oscillators. Transport due to chaos is an important problem
in Hamiltonian dynamics also. A recent approach is to evaluate the exact diffusion
coefficient in terms of the periodic orbits of the system in the form of cycle
expansions. But the fact is that the chaotic motion in such spatially extended maps
has two complementary aspects- - diffusion and interrnittency. These are related
to the time evolution of the probability density function which is approximately
Gaussian by central limit theorem. It is noticed that the characteristic function
method introduced by Fujisaka and his co-workers is a very powerful tool for
analysing both these aspects of chaotic motion. The theory based on characteristic
function actually provides a thermodynamic formalism for chaotic systems
It can be applied to other types of chaos-induced diffusion also, such as the one
arising in statistics of trajectory separation. It was noted that there is a close connection
between cycle expansion technique and characteristic function method. It
was found that this connection can be exploited to enhance the applicability of
the cycle expansion technique. In this way, we found that cycle expansion can be
used to analyse the probability density function in chaotic maps. In our research
studies we have successfully applied the characteristic function method and cycle
expansion technique for analysing some chaotic maps. We introduced in this
connection, two classes of chaotic maps with variable shape by generalizing two
types of maps well known in literature.
Description:
Department of Physics, Cochin University of Science and Technology