PřF:M0200 Symplectic systems - Course Information
M0200 Symplectic systems
Faculty of ScienceSpring 2015
- Extent and Intensity
- 2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: z (credit).
- Teacher(s)
- doc. Mgr. Petr Zemánek, Ph.D. (lecturer)
- Guaranteed by
- prof. RNDr. Roman Šimon Hilscher, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. Mgr. Petr Zemánek, Ph.D.
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Thu 14:00–15:50 MS1,01016
- Prerequisites
- No special prerequisites are required (basic courses of the calculus and linear algebra are sufficient).
- Course Enrolment Limitations
- The course is offered to students of any study field.
- Course objectives
- Ths course is devoted to the theory of symplectic systems. At the end of the course students should be able to: to define and interpret the basic notions, to formulate relevant mathematical theorems and to explain methods of their proofs.
- Syllabus
- This course is devoted to discrete symplectic systems. We focus on its basic properties, oscillation theory, spectral theory, and the number of square summable solutions.
- Literature
- ZEMÁNEK, Petr. Symplektické diferenční systémy (Symplectic Difference Systems). Brno: Masarykova univerzita, 2007. Diplomová práce. URL info
- DOŠLÝ, Ondřej and Martin BOHNER. Disconjugacy and transfomations for symplectic systems. Rocky Mountain Journal of Mathematics. 1997, vol. 27, No 2, p. 707-743. ISSN 0035-7596. info
- BOHNER, Martin, Ondřej DOŠLÝ and Werner KRATZ. Sturmian and spectral theory for discrete symplectic systems. Trans. Amer. Math. Soc. 2009, vol. 361, No 6, p. 3109-3123. ISSN 0002-9947. URL info
- ZEMÁNEK, Petr. Discrete trigonometric and hyperbolic systems: An overview. Ulm: University of Ulm, 2009, 14 pp. URL info
- CLARK, Stephen L and Petr ZEMÁNEK. On a Weyl-Titchmarsh theory for discrete symplectic systems on a half line. Applied Mathematics and Computation. Spojené státy americké: Elsevier, 2010, vol. 217, No 7, p. 2952-2976. ISSN 0096-3003. URL info
- ŠIMON HILSCHER, Roman and Petr ZEMÁNEK. Weyl-Titchmarsh theory for discrete symplectic systems with general linear dependence on spectral parameter. Journal of Difference Equations and Applications. Taylor and Francis, 2014, vol. 20, No 1, p. 84-117. ISSN 1023-6198. Available from: https://dx.doi.org/10.1080/10236198.2013.813496. info
- ŠIMON HILSCHER, Roman and Petr ZEMÁNEK. Overview of Weyl-Titchmarsh theory for second order Sturm-Liouville equations on time scales. Int. J. Difference Equ. Delhi: Research India Publications, 2011, vol. 6, No 1, p. 39-51. ISSN 0973-6069. info
- ŠIMON HILSCHER, Roman and Petr ZEMÁNEK. Limit circle invariance for two differential systems on time scales. Mathematische Nachrichten. Akademie-Verlag, 2015, vol. 288, 5-6, p. 696-709. ISSN 0025-584X. Available from: https://dx.doi.org/10.1002/mana.201400005. info
- ZEMÁNEK, Petr. New Results in Theory of Symplectic Systems on Time Scales. první. Brno: Masarykova univerzita, 2011, 98 pp. ISBN 978-80-210-5515-5. info
- ŠIMON HILSCHER, Roman and Petr ZEMÁNEK. Time scale symplectic systems with analytic dependence on spectral parameter. Journal of Difference Equations and Applications. London: Taylor and Francis, 2015, vol. 21, No 3, p. 209-239. ISSN 1023-6198. Available from: https://dx.doi.org/10.1080/10236198.2014.997227. info
- Teaching methods
- Theoretical lecture 2 hours per week.
- Assessment methods
- Credits will be given according to the attendance record.
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught only once.
- Enrolment Statistics (recent)
- Permalink: https://is.muni.cz/course/sci/spring2015/M0200