World Scientific series in Applicable Analysis (WSSIAA) aims at reporting new developments of high mathematical standard and current interest. Each volume in the series shall be devoted to the mathematical analysis that has been applied or potentially applicable to the solutions of scientific, engineering and social problems. For the past 25 years, there has been an explosion of interest in the study of nonlinear dynamical systems. Mathematical techniques developed during this period have been applied to important nonlinear problems ranging from physics and chemistry to ecology and economics. All these developments have made dynamical systems theory an important and attractive branch of mathematics to scientists in many disciplines. This rich mathematical subject has been partially represented in this collection of 45 papers by some of the leading researchers in the area. This volume contains 45 state-of-the-art articles on the mathematical theory of dynamical systems by leading researchers. It is hoped that this collection will lead new direction in this field Wolfgang Walter / R.M. Redheffer -- On free boundary problems for quasi-linear elliptic PDE's: Uniqueness and monotone ordering of convex solutions / A. Acker -- On the determination of price and quantity indices and their monotonicity / J.D. Aczel and R. Girgensohn -- An inverse isoperimetric comparison result / A. Alvino, V. Ferone, B. Kawohl and G. Trombetti -- Stabilizing the backward heat equation against errors in the initial time geometry / K.A. Ames and L.E. Payne -- Canonical products of genus two / Y. Avishai and R.M. Redheffer -- Asymptotic behaviour and convexity of large solutions to nonlinear equations / C. Bandle and G. Porru -- Two integral inequalities / B.M. Brown, W.D. Evans, W.N. Everitt and V.G. Kirby -- An interpolation inequality and applications / R.C. Brown and D.B. Hinton -- On the best constant for the inequality [actual symbol not reproducible] / R.C. Brown and M.K. Kwong -- On functions convex with respect to an N-parameter family of functions / D. Brydak