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The book deals with dynamical systems, generated by linear mappings of finite dimensional spaces and their applications. These systems have a relatively simple structure from the point of view of the modern dynamical systems theory. However, for the dynamical systems of this sort, it is possible to obtain explicit answers to specific questions being useful in applications.

The considered problems are natural and look rather simple, but in reality in the course of investigation, they confront users with plenty of subtle questions and their detailed analysis needs a substantial effort.

The problems arising are related to linear algebra and dynamical systems theory, and therefore, the book can be considered as a natural amplification, refinement and supplement to linear algebra and dynamical systems theory textbooks.

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Introduction.- Vector trajectory.- The Jordan basis and special subspaces.- Representation of the vector trajectory.- The structures related to the principal term of the vector Trajectory.- The asymptotic behavior of vector trajectories and trajectories of one-dimensional subspaces.- The geometric approach.- The geometric approach: an operator with one point spectrum.- The convergence of a subspace trajectory for an arbitrary operator.- The applications to weighted shift operators.- The spectrum of weighted shift operator.- The subtle spectral properties.- The weighted shift operators in spaces of vector functions.

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From the book reviews:
"This is an excellent book that can be used for a third or fourth year graduate course in dynamical systems or a related field. ... there is a good solid bibliography and pertinent references (both books and journal articles) making the book ideal for a seminar type presentation where students participate in the course with presentation of papers." (Russell Jay Hendel, MAA Reviews, January, 2015)

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Cemal B. Dolicanin (Cemal B. Dolicanin), full Professor of Mathematics at the State University of Novi Pazar, Republic of Serbia. He is a member of South Slavic Academy of Non-linear Sciences (JANN). He published 90 scientific papers in Theoretical Mathematics, Geometry, Dynamical Systems Theory and Applied Mathematics in Engineering Sciences. Applications from these papers are published in 26 textbooks and monographs.
e-mail: cdolicanin@np.ac.rs

Anatolij B. Antonevich, full Professor of Mathematics at Belarusian State University, Minsk, Belarus and he is a Professor of Mathematics at the University of Bialystok, Poland. He is the author of 250 scientific papers in Functional Analysis and its applications are published in 15 monographs and textbooks.
e-mail: antonevich@bsu.by

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