On Chaos and Fractals in General Topological Spaces

The present study on chaos and fractals in general topological spaces. Chaos theory originated with the work of Edward Lorenz. The phenomenon which changes order into disorder is known as chaos. Theory of fractals has its origin with the frame work of Benoit Mandelbrot in 1977. Fractals are irregular objects. In this study different properties of topological entropy in chaos spaces are studied, which also include hyper spaces. Topological entropy is a measures to determine the complexity of the space, and compare different chaos spaces. The concept of fractals can’t be extended to general topological space fast it involves Hausdorff dimensions. The relations between hausdorff dimension and packing dimension. Regular sets in Metric spaces using packing measures, regular sets were defined in IR” using Hausdorff measures. In this study some properties of self similar sets and partial self similar sets. We can associate a directed graph to each partial selfsimilar set. Dimension properties of partial self similar sets are studied using this graph. Introduce superself similar sets as a generalization of self similar sets and also prove that chaotic self similar self are dense in hyper space. The study concludes some relationships between different kinds of dimension and fractals. By defining regular sets through packing dimension in the same way as regular sets defined by K. Falconer through Hausdorff dimension, and different properties of regular sets also.

Resource abundance and Survival of indigenous ornamental fishes of central Kerala with emphasis on handling and packing stress in Puntius filamentosus(VALENCIENNES)

This thesis Entitled Resource abundance and survival of indigenous ornamental fishes of central kerala with emphasis on handling and packing stress in puntius filamentosus (valenciennes).Kerala state is endowed with 41 west flowing and three east flowing rivers originating in the Western Ghats. These rivers and their vast network of tributaries and distributaries harbour rich and diversified fish fauna. Most of the freshwater fishes available in Kerala are highly appreciated as ornamental fishes in the national and international markets.Today the ornamental fish industry is one of the largest industries all over the world. The demand for ornamental fishes has been increasing steadily with the enlargement of the industry, such that the current demand for indigenous ornamental fishes have exceeded the supply. This has led to serious concern about the resources available in the country that can be utilised judiciously for the economic benefit of the state. With an aim to fill up the lacuna, a database of freshwater ornamental fishes of Kerala was created as part of the present study. Ornamental fishes destined for export marketing should thrive well in the aquarium conditions.The study reiterates fishes caught from different environmental conditions and feeding habits have a greater ability to adapt and acclimatise to an entirely new environment and food habits. Marketing studies based on the statistics available with Marine Products Export Development Authority show that these species are not being exported at the required level over the past 6 years, when compared to the availability in the water bodies of Kerala. Sustainable utilisation of these resources from the wild using modern management principles and code of conduct for responsible fishing are advisable until captive breeding technology is popularised.