Scaling relations in the Lyapunov exponents of one dimensional maps

We establish numerically the validity of Huberman-Rudnick scaling relation for Lyapunov exponents during the period doubling route to chaos in one dimensional maps. We extend our studies to the context of a combination map. where the scaling index is found to be different.

Investigations on the Dynamics of Combination Maps and the Analysis of Bifurcation in a Discontinuous Logistic Map

This thesis is a study of discrete nonlinear systems represented by one dimensional mappings.As one dimensional interative maps represent Poincarre sections of higher dimensional flows,they offer a convenient means to understand the dynamical evolution of many physical systems.It highlighting the basic ideas of deterministic chaos.Qualitative and quantitative measures for the detection and characterization of chaos in nonlinear systems are discussed.Some simple mathematical models exhibiting chaos are presented.The bifurcation scenario and the possible routes to chaos are explained.It present the results of the numerical computational of the Lyapunov exponents (λ) of one dimensional maps.This thesis focuses on the results obtained by our investigations on combinations maps,scaling behaviour of the Lyapunov characteristic exponents of one dimensional maps and the nature of bifurcations in a discontinous logistic map.It gives a review of the major routes to chaos in dissipative systems,namely, Period-doubling ,Intermittency and Crises.This study gives a theoretical understanding of the route to chaos in discontinous systems.A detailed analysis of the dynamics of a discontinous logistic map is carried out, both analytically and numerically ,to understand the route it follows to chaos.The present analysis deals only with the case of the discontinuity parameter applied to the right half of the interval of mapping.A detailed analysis for the n –furcations of various periodicities can be made and a more general theory for the map with discontinuities applied at different positions can be on a similar footing

Analytical Studies on Diffusion and lntermittency in Chaotic Maps

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.

Chaos in modulated logistic systems

This paper is a review of the work done on the dynamics of modulated logistic systems. Three different problems are treated, viz, the modulated logistic map, the parametrically perturbed logistic map and the combination map obtained by combining two maps of the quadratic family. Many of the interesting features displayed by these systems are discussed.

“Rights of Women against Domestic Violence - The Law and Emerging Challenges”

Domestic violence is a gender based violation of human rights having multi- dimensional repercussions in the well- being of individuals in family and society. The Indian legislation to protect the women from domestic violence is significant in providing a mechanism for enforcing positive civil rights of protection and injunction orders to the victims of domestic violence along with the existing remedies of criminal sanctions. However the Act was brought in the backdrop of an established tradition of cohesive and stable family setting. This, in turn, results in the emergence of new issues and challenges which necessitates deeper understandings of indigenous sociocultural institutions in India i.e., marriage and family. This study is an attempt to analyse the Indian law on domestic violence and to assess whether the law addresses and answers the problems of domestic violence effectively in the culture specific setting of India

Challenges Faced by Kerala Tourism Industry

Tourism being a smokeless industry is now a multi-billion, multi-sectoral and multi-dimensional activity in the world. Twenty first century tourism has reached up to space when a Russian rocket carried the space vehicle of Dennis Tito, an American businessman and the world’s first space tourist, to the space station. Time is not too far to carry tourists to moon and other planets in specially launched vehicles. Tourism is being considered as an agent of social change bridging gaps among nations, regions and people and helping them to open up. It is a promoter of development-material and spiritual both at macro and micro level. The General Assembly of the United Nations, in designating the year 1967 as ‘International Tourism Year’ recognized the importance of international travel as a means of fostering understanding among people, and giving them a knowledge of the rich heritage of the past civilizations, a better appreciation of the values of different cultures, thus contributing to the strengthening of world peace. It adopted the theme “Tourism-Passport to peace”. Our veteran national leader and the first Prime Minister of India, Jawaharlal Nehru had said” welcome a tourist and send back a friend” which indicates the need for extending friendly hospitality to the in bound tourists. Modern transportation has removed the obstacles of distance enabling people to appreciate each other engage in the exchange of ideas and commerce. Tourism can help overcome real prejudices and foster bonds. Tourism can be a real force of world peace. Considering the vast and varied potential of tourism in the state and its impact on the economic, social and cultural environment of the state, a detailed study is found to be relevant and imperative

Strategies for Inverse Profiling of Two Dimensional Dielectric Scatterers Using Electromagnetic Illumination

Electromagnetic tomography has been applied to problems in nondestructive evolution, ground-penetrating radar, synthetic aperture radar, target identification, electrical well logging, medical imaging etc. The problem of electromagnetic tomography involves the estimation of cross sectional distribution dielectric permittivity, conductivity etc based on measurement of the scattered fields. The inverse scattering problem of electromagnetic imaging is highly non linear and ill posed, and is liable to get trapped in local minima. The iterative solution techniques employed for computing the inverse scattering problem of electromagnetic imaging are highly computation intensive. Thus the solution to electromagnetic imaging problem is beset with convergence and computational issues. The attempt of this thesis is to develop methods suitable for improving the convergence and reduce the total computations for tomographic imaging of two dimensional dielectric cylinders illuminated by TM polarized waves, where the scattering problem is defmed using scalar equations. A multi resolution frequency hopping approach was proposed as opposed to the conventional frequency hopping approach employed to image large inhomogeneous scatterers. The strategy was tested on both synthetic and experimental data and gave results that were better localized and also accelerated the iterative procedure employed for the imaging. A Degree of Symmetry formulation was introduced to locate the scatterer in the investigation domain when the scatterer cross section was circular. The investigation domain could thus be reduced which reduced the degrees of freedom of the inverse scattering process. Thus the entire measured scattered data was available for the optimization of fewer numbers of pixels. This resulted in better and more robust reconstructions of the scatterer cross sectional profile. The Degree of Symmetry formulation could also be applied to the practical problem of limited angle tomography, as in the case of a buried pipeline, where the ill posedness is much larger. The formulation was also tested using experimental data generated from an experimental setup that was designed. The experimental results confirmed the practical applicability of the formulation.