Module also offered within study programmes:
General information:
Name:
Dynamical systems
Course of study:
2019/2020
Code:
ZSDA-3-0255-s
Faculty of:
Szkoła Doktorska AGH
Study level:
Third-cycle studies
Specialty:
-
Field of study:
Szkoła Doktorska AGH
Semester:
0
Profile of education:
Academic (A)
Lecture language:
English
Form and type of study:
Full-time studies
Course homepage:
 
Responsible teacher:
prof. dr hab. Oprocha Piotr (oprocha@agh.edu.pl)
Dyscypliny:
matematyka
Module summary

The aim of seminar is presentation and discussion on recent advances in the field of discrete dynamical systems, understood in wide sense (topological dynamics, ergodic theory, symbolic dynamics, etc.).

Description of learning outcomes for module
MLO code Student after module completion has the knowledge/ knows how to/is able to Connections with FLO Method of learning outcomes verification (form of completion)
Skills: he can
M_U001 Student is able to present advanced research topics (theorems, examples, techniques, results of simulations) in front of audience made of specialists in clear and mathematically strict way. SDA3A_U02 Activity during classes
Knowledge: he knows and understands
M_W001 Student is able to describe in general terms a few important research directions in modern theory of dynamical systems, that were recently conducted in good academic centers and published in best mathematical journals. SDA3A_W02, SDA3A_U02 Activity during classes
M_W002 Student is able to understand and present advanced theorems, examples and techniques related to theory of dynamical systems and ergodic theory. SDA3A_U01
M_W003 Student is able to distinguish between different levels of research topics (easy, hard; trivial, good, excellent). He/she is aware level research expected for publication in best mathematical journals. SDA3A_K01 Activity during classes
Number of hours for each form of classes:
Sum (hours)
Lecture
Audit. classes
Lab. classes
Project classes
Conv. seminar
Seminar classes
Pract. classes
Zaj. terenowe
Zaj. warsztatowe
Prace kontr. przejść.
Lektorat
30 0 0 0 0 0 30 0 0 0 0 0
FLO matrix in relation to forms of classes
MLO code Student after module completion has the knowledge/ knows how to/is able to Form of classes
Lecture
Audit. classes
Lab. classes
Project classes
Conv. seminar
Seminar classes
Pract. classes
Zaj. terenowe
Zaj. warsztatowe
Prace kontr. przejść.
Lektorat
Skills
M_U001 Student is able to present advanced research topics (theorems, examples, techniques, results of simulations) in front of audience made of specialists in clear and mathematically strict way. - - - - - + - - - - -
Knowledge
M_W001 Student is able to describe in general terms a few important research directions in modern theory of dynamical systems, that were recently conducted in good academic centers and published in best mathematical journals. - - - - - + - - - - -
M_W002 Student is able to understand and present advanced theorems, examples and techniques related to theory of dynamical systems and ergodic theory. - - - - - + - - - - -
M_W003 Student is able to distinguish between different levels of research topics (easy, hard; trivial, good, excellent). He/she is aware level research expected for publication in best mathematical journals. - - - - - + - - - - -
Student workload (ECTS credits balance)
Student activity form Student workload
Summary student workload 60 h
Module ECTS credits 2 ECTS
Udział w zajęciach dydaktycznych/praktyka 30 h
Preparation for classes 10 h
Realization of independently performed tasks 15 h
Contact hours 5 h
Module content
Seminar classes (30h):
-
Additional information
Teaching methods and techniques:
  • Seminar classes: Presentation or research results. Discussion.
Warunki i sposób zaliczenia poszczególnych form zajęć, w tym zasady zaliczeń poprawkowych, a także warunki dopuszczenia do egzaminu:

Mark based on evaluation of the presentation and the activity in discussions

Participation rules in classes:
  • Seminar classes:
    – Attendance is mandatory: Yes
    – Participation rules in classes: Presentation and discussion on selected recent research publications in the field of dynamical systems.
Method of calculating the final grade:

Mark based on evaluation of the presentation and the activity in discussions

Sposób i tryb wyrównywania zaległości powstałych wskutek nieobecności studenta na zajęciach:

The student should report to the lecturer to determine the individual way of catching up.

Prerequisites and additional requirements:

Student has knowledge of mathematical analysis, topology and measure theory at a level of standard undergraduate courses.

Recommended literature and teaching resources:

1. R. Devaney, An introduction to chaotic dynamical systems, Second edition, Studies in Nonlinearity, Addison-Wesley Publishing Company, Redwood City, 1989.
2. C. Robinson, Dynamical systems. Stability, symbolic dynamics and chaos, Second edition, CRC Press, Boca Raton, 1999.
3. P. Walters, An introduction to ergodic theory, Springer-Verlag, New York-Berlin, 1982.
4. Kůrka, Petr. Topological and symbolic dynamics. Cours Spécialisés [Specialized Courses], 11. Société Mathématique de France, Paris, 2003.
5. Einsiedler, Manfred; Ward, Thomas. Ergodic theory with a view towards number theory. Graduate Texts in Mathematics, 259. Springer-Verlag London, Ltd., London, 2011.
6. Aoki, N.; Hiraide, K. Topological theory of dynamical systems. Recent advances. North-Holland Mathematical Library, 52. North-Holland Publishing Co., Amsterdam, 1994

Scientific publications of module course instructors related to the topic of the module:
P. Oprocha, P. Potorski, P. Raith, “Mixing properties in expanding Lorenz maps”, Adv. Math., 343 (2019), 712-755.

J. Boroński, J. Kupka and P. Oprocha, “Mixing completely scrambled system exists”, Erg. Th. Dynam. Syst., 39 (2019), 62-73.

P. Oprocha, “Double minimality, entropy and disjointness with all minimal systems”, Discrete Contin. Dyn. Syst., 39 (2019), 263—275.

C. Good, P. Oprocha, M. Puljiz, “Shadowing, asymptotic shadowing and s-limit shadowing”, Fund. Math., 244 (2019), 287-312.

J. Boroński, A. Clark and P. Oprocha, “A compact minimal space Y such that its square YxY is not minimal”, Adv. Math., 335 (2018), 261-275.

W. Brian, P. Oprocha,“Ultrafilters and Ramsey-type shadowing phenomena in topological dynamics”, Israel J. Math., 227 (2018), 423-453.

Y. Dong, P. Oprocha and X. Tian, “On the irregular points for systems with the shadowing property”, Erg. Th. Dynam. Syst.,28 (2018), 2108-2131.

Additional information:

None