FEDORKOVÁ, L. Stability and stabilization of autonomous difference systems [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2024.
The student Lucie Fedorková prepared her Ph.D. work on problems of stability and stabilization of autonomous difference equations. A substantial part of her dissertation is devoted to the related area, namely a profound root analysis of real and complex polynomials (particularly trinomials). Despite many existing works on this classical topic, the student has obtained several new key results in the polynomial area. These results form the base of three of her papers (two of them are already published in impact journals, and the third one, submitted in October 2023 to the Pacific Journal of Mathematics, is, after a round of positive reviews (with mainly formal recommendations), still waiting for the final editorial decision. In the second part of the dissertation, the obtained polynomial results are applied to the qualitative theory of difference equations, with an emphasis put on the stability, asymptotic, and periodicity properties of studied equations. The corresponding results are summarized in two papers, which are currently being finalized. I would like to express my appreciation for the student's responsible approach to preparing this dissertation, as well as her interest in the topic studied. Despite her maternity duties (accompanied by restrictions during the Covid time), she worked very intensively in the area of her dissertation and finished this work after 5 years of Ph.D study. The student's main original scientific contribution consists primarily in the performance of demanding computational analysis of the studied problems. To answer the issues posed, she had to become acquainted with tools of qualitative investigations of difference equations, including parts of complex analysis, matrix theory, and elementary number theory. Besides the scientific contribution to the topic of this dissertation, the student's activities also included didactical aspects. In particular, she became the co-author of a paper devoted to the life and work of outstanding Latvian mathematician Pierse Bohl, whose (nearly forgotten) results turned out to be relevant in her investigations. This paper has been accepted for publication in the journal Pokroky matematiky, fyziky and astronomie (edited by The Union of Czech Mathematicians and Physicists), and its part is also included in this dissertation. Based on these facts, I recommend this dissertation for defense.
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eVSKP id 163109