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Regular version of the site
Master 2021/2022

Differential equations on manifolds

Type: Compulsory course (Mathematics)
Area of studies: Mathematics
When: 1 year, 1, 2 module
Mode of studies: offline
Open to: students of one campus
Instructors: Natalya Stankevich
Master’s programme: Mathematics
Language: English
ECTS credits: 6
Contact hours: 60

Course Syllabus

Abstract

Differential equations on manifolds is a half-year course for the first-year students of master degree in mathematics. It is based on courses of Mathematical Analysis, Linear Algebra and Topology. The course is devoted to studying of classical and modern methods of qualitative theory of dynamical systems in manifolds and prepares students for understanding further courses Ergodic Theory, Theory of Local Bifurcations, Modern Theory of Dynamical Systems.
Learning Objectives

Learning Objectives

  • Studying of basic methods of qualitative theory and important classes od dynamical systems on manifolds: local and global analysis, hyperbolic points and sets, energy function, Morse-Smale systems, hyperbolic systems.
Expected Learning Outcomes

Expected Learning Outcomes

  • A student knows motivation and basic technics of the topic, is able to apply his knowledge to solution of textbook problems and confidently use a terminology of the subject.
Course Contents

Course Contents

  • Topology of manifolds and vector fields on manifolds.
  • Local analysis.
  • Hyperbolic dynamics.
  • Morse-Smale Systems
Assessment Elements

Assessment Elements

  • non-blocking контрольная работа
  • non-blocking итоговый опрос по разделу
  • non-blocking итоговый опрос
Interim Assessment

Interim Assessment

  • 2021/2022 1st module
    0.7 * итоговый опрос по разделу + 0.3 * контрольная работа
  • 2021/2022 2nd module
    0.3 * контрольная работа + 0.7 * итоговый опрос по разделу
Bibliography

Bibliography

Recommended Core Bibliography

  • Shilnikov L.P., Shilnikov A.L., Turaev D.V., Chua L.O. Methods Of Qualitative Theory In Nonlinear Dynamics (Part II). World Sci //Singapore, New Jersey, London, Hong Kong. – 2001.

Recommended Additional Bibliography

  • Grines V., Medvedev Timur, Pochinka O. Dynamical Systems on 2- and 3-Manifolds. Switzerland : Springer, 2016.