Adıvar, Murat; Raffoul, Youssef N. Stability, periodicity and boundedness in functional dynamical systems on time scales. (English) Zbl 1464.34001 Cham: Springer (ISBN 978-3-030-42116-8/hbk; 978-3-030-42117-5/ebook). xiv, 416 p. (2020). This book contains recent developments of the qualitative theory of stability, periodicity and boundedness of functional dynamical systems on time scales. It consists of a Preface, 8 Chapters, a Bibliography and an Index. The aim of the book is presented in the Preface. Chapter 1 consists of the introduction to stability and boundedness in dynamical systems, where a brief introduction to time scale calculus and fundamental concepts needed throughout the book are provided. Chapter 2 is dealing with ordinary dynamical systems, Chapter 3 with functional dynamical systems, while Volterra integro-dymanic equations with or without delay are studied in Chapter 4. The construction of exotic Lyapunov functionals for the study of boundedness and stabilty is presented in Chapter 5, while Volterra integral dynamic equations are studied in Chapter 6. Chapter 7 is dealing with periodic solutions and in Chapter 8 periodic solutions of functional delay dynamic systems, where the periodic delays are expressed in terms of shift operators, are studied. The Bibliography consists of 169 entries. This book is organized in the classical mathematical style: definitions, lemmata, theorems, corollaries, proofs, examples, remarks, applications, etc. In each chapter, several examples are solved and open problems, which should be of great benefit to the researchers on the subject, are proposed. The book is well written and reads very well. It provides a useful reference in the field. Reviewer: Ioannis P. Stavroulakis (Ioannina) Cited in 3 Documents MSC: 34-02 Research exposition (monographs, survey articles) pertaining to ordinary differential equations 45-02 Research exposition (monographs, survey articles) pertaining to integral equations 34N05 Dynamic equations on time scales or measure chains 34D20 Stability of solutions to ordinary differential equations 34C25 Periodic solutions to ordinary differential equations 34C11 Growth and boundedness of solutions to ordinary differential equations 39-02 Research exposition (monographs, survey articles) pertaining to difference and functional equations 34K42 Functional-differential equations on time scales or measure chains Keywords:stability; periodicity; boundedness; functional dynamical systems; time scales; Volterra integro-dynamic equations; differential equations; difference equations PDFBibTeX XMLCite \textit{M. Adıvar} and \textit{Y. N. Raffoul}, Stability, periodicity and boundedness in functional dynamical systems on time scales. Cham: Springer (2020; Zbl 1464.34001) Full Text: DOI