The book "On recurrent trajectories, minimum sets" by the authors Afanasyev A. P. and Juba C. M. It is a fascinating and in-depth study in the field of mathematical theory of dynamical systems. This work will be a real discovery for those who are interested in mathematics, physics, as well as related sciences, such as computer science and biology. The authors, having rich experience in their field, offer readers a unique view of complex concepts, making them accessible and understandable. The book focuses on recurrent trajectories and minimal sets that play a key role in the study of dynamical systems. Recurrent trajectories are sequences of states of a system that repeat over time, and minimal sets are the optimal structures on which these trajectories are concentrated. The authors examine in detail how these concepts intersect and influence the behavior of systems in various fields of science. The book will be of interest not only to professional mathematicians and physicists, but also to students, graduate students, as well as anyone who seeks a deeper understanding of dynamic processes in nature and technology. If you are interested in topics such as chaos theory, nonlinear dynamical systems or mathematical modeling, this work will become a real storehouse of knowledge for you. Readers interested in books such as Edward Lorentz's Chaos Theory or Stephen Strogatz's Nonlinear Dynamical Systems will find many parallels and new ideas in On Recurrent Trajectories, Minimum Sets. The topics raised in the book cover a wide range of issues, including the stability of dynamical systems, the properties of recurrent trajectories and their application in various scientific disciplines. The authors not only present theoretical foundations, but also illustrate their ideas with practical examples, which makes the material more clear and understandable. This allows readers not only to assimilate information, but also to apply it in their research and practice. The writing style of Afanasiev and Dziuba is clear and logical . They skillfully balance between strict mathematical formulation and accessible presentation, which makes the book interesting both for specialists and for a wide audience. Their previous works, such as “Dynamics of Complex Systems” and “Mathematical Models in Biology”, have already established themselves as valuable sources of knowledge, and the new book will not be an exception. “On recurrent trajectories, minimum sets” is not just a textbook, but a real find for anyone who wants to deepen their knowledge in the field of dynamical systems. The book encourages readers to reflect on how mathematical concepts can be applied to real-world problems, and inspires further research. If you are looking for a work that combines theory and practice, and also offers a fresh perspective on familiar topics, this book will be an excellent choice. Do not miss the opportunity to immerse yourself in the world of recurrent trajectories and minimal sets, discovering new horizons of science and mathematics. “On recurrent trajectories, minimum sets” is a book that will not only enrich your knowledge, but also inspire new ideas and research.