Foundations of Iso-Differential Calculus. Volume 4: Iso-Dynamic Equations


Svetlin G. Georgiev
Sorbonne University, Paris, France
Faculty of Mathematics and Informatics, Department of Differential Equations, Sofia University, Sofia, Bulgaria

Series: Mathematics Research Developments
BISAC: MAT005000

This book is intended for readers who have had or currently have a course in difference equations or iso-differential calculus. It can be used for a senior undergraduate course. Chapter 1 deals with the linear first-order iso-difference equations, equilibrium points, eventually equilibrium points, periodic points and cycles. Chapter 2 are introduces iso-difference calculus and the general theory of the linear homogeneous and nonhomogeneous iso-difference equations. Chapter 3 studies the systems of linear iso-difference equations and the linear periodic systems. Chapter 4 is devoted to the stability theory.

They are considered the nonautonomous linear systems, Lyapunov’s direct method, and stability by linear approximation. Chapter 5 discusses the oscillation theory. The oscillation theory is defined as the iso-self-adjoint second-order iso-difference equations and they are given some of their properties. They are considered some classes of nonlinear iso-difference equations. Chapter 6 studies the asymptotic behavior of some classes of iso-difference equations. Time scales iso-calculus is introduced in Chapter 7. They are given the main properties of the backward and forward jump iso-operators. They are considered the iso-differentiation and iso-integration. They are introduced as the iso-Hilger’s complex plane and the iso-exponential function (Imprint: Nova)



Table of Contents


Chapter 1 – Introduction (pp. 1-22)

Chapter 2 – Linear Iso-Difference Equations of Higher Order (pp. 23-66)

Chapter 3 – Systems of Linear Iso-Difference Equations (pp. 67-88)

Chapter 4 – Stability Theory (pp. 89-128)

Chapter 5 -Oscillation Theory (pp. 129-152)

Chapter 6 – Asymptotic Behavior of Iso-Difference Equations (pp. 153-166)

Chapter 7 – Time Scales Iso-Calculus (pp. 167-224)

Chapter 8 – Appendix (pp. 225-260)



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