M0200 Symplectic systems

Faculty of Science
Spring 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. Diplomová práce. 2007. URL info
  • DOŠLÝ, Ondřej and Martin BOHNER. Disconjugacy and transfomations for symplectic systems. Rocky Mountain Journal of Mathematics. vol. 27, No 2, p. 707-743. ISSN 0035-7596. 1997. info
  • BOHNER, Martin, Ondřej DOŠLÝ and Werner KRATZ. Sturmian and spectral theory for discrete symplectic systems. Trans. Amer. Math. Soc. vol. 361, No 6, p. 3109-3123. ISSN 0002-9947. 2009. URL info
  • ZEMÁNEK, Petr. Discrete trigonometric and hyperbolic systems: An overview. Ulm: University of Ulm. 14 pp. 2009. 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, vol. 217, No 7, p. 2952-2976. ISSN 0096-3003. 2010. 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, vol. 20, No 1, p. 84-117. ISSN 1023-6198. doi:10.1080/10236198.2013.813496. 2014. 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, vol. 6, No 1, p. 39-51. ISSN 0973-6069. 2011. info
  • ŠIMON HILSCHER, Roman and Petr ZEMÁNEK. Limit circle invariance for two differential systems on time scales. Mathematische Nachrichten. Akademie-Verlag, vol. 288, 5-6, p. 696-709. ISSN 0025-584X. doi:10.1002/mana.201400005. 2015. info
  • ZEMÁNEK, Petr. New Results in Theory of Symplectic Systems on Time Scales. první. Brno: Masarykova univerzita. 98 pp. ISBN 978-80-210-5515-5. 2011. 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, vol. 21, No 3, p. 209-239. ISSN 1023-6198. doi:10.1080/10236198.2014.997227. 2015. 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