In recent times, theory of difference equations has assumed a greater importance as a well deserved discipline because of several reasons. Although there is a striking duality between the theories of differential equations and difference equations, the theory of difference equations is a lot richer than the corresponding theory of differential equations, and often demands additional assumptions to overcome the topological deficiency of lacking connectedness. None the less, it is natural to seek a framework which permits us to handle both dynamic systems simultaneously in order to get better insight and understanding of the subtle differences of the two systems. Recently developed theory of dynamic systems on time scales (closed sets of reals) provides the desired unified approach.
KeywordsTopological Space Difference Equation Order Topology Jump Operator Induction Principle
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