The thesis deals with analysis of a discrete logistic equation which in contrast to its continuous couterpart exhibits very complex dynamics. In particular, the following topics are treated within the study of the logistic map: stability of equilibria, periodic cycles and period-doubling, bifurcation, tent map, conjugacy, chaotic behavior, and Lyapunov exponents.

I really appreciate the student's independence in working on a difficult topic. He performed many analytic computations and also numerical simulations. Even in some parts which serve just as a description of supporting tools (and students here typically simply copy a relevant text from the literature), the author tried to bring his own contribution. English is very good.
As for the problematic points, in particular Chapter 4 should deserve some revision. Further, quotation of sources is not faultless. There are some typos and other imperfections. But they are mostly of minor character.

The author demonstrated the ability to work on an advanced topic and created an interesting text which offers quite many qualitative as well as quantitative aspects of logistic map.

The main goals have been achieved, and in view of the above said I can recommend the thesis for defense with overall classification B = very good.

The present thesis is focused to the analysis of the logistic equation, iterations in the real line, and chaotic dynamic.

I would like to appreciate:

1. The author composed a consistent and meaningful text concerning quite difficult topic.
2. The thesis has the logical structure, all discussed notions are illustrated by numerical simulations.
3. Namely, Section 3.1 concerning the periodic orbits of the logistic equation is written very well.

On the other hand, I have some objections, in particular:

1. Citations to the list of references are missing in the whole text. The author formulates lemmas and propositions without proofs and citations to the literature.
2. The text contains some mathematical inaccuracies which is, however, standard in such a type of students' works (e.g., discussion concerning the behaviour of iterates on p. 16, comparison of equations (2.4) and (2.5), arrows in figure 9, connection between the existence of a dense orbit and density of the set of periodic points).
3. Definitions of some notions are missing (e.g., basin of attraction for the orbit).

Conclusion: The author demonstrated the ability to work on a difficult topic, compose a meaningful text, and accomplish some numerical simulations. In my opinion, main goals of the thesis have been achieved. In view of the above-said, I can recommend the thesis for defense and I propose the evaluation B. Topics for thesis defence:

1. Why do you assume for further analysis on p. 25 that \mu\geq1?