Research Seminar " Dynamics of Endomorphisms"

2024/2025

Academic Year

ENG

Instruction in English

6

ECTS credits

Delivered at:

Department of Fundamental Mathematics (Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod))

Course type:

Compulsory course

When:

2 year, 1, 2 module

Instructor

Zhuzhoma, Evgeny V.

Course Syllabus

Abstract

The course deals with the basic concepts and methods of studying endomorphisms given on manifolds. This program sets the minimum requirements for the knowledge and skills of master's students studying in the direction of 01.04.01 Mathematics.

Learning Objectives

• The purpose of studying the discipline is to master the methods for studying the dynamics of endomorphisms of low-dimensional manifolds.

Expected Learning Outcomes

• Know examples of Anosov endomorphisms on multidimensional tori
• Know the definition of endomorphism

Course Contents

• Basic definitions and examples
• Bifurcations of Anosov endomorphisms

Assessment Elements

• Контрольная
• Экзамен

Interim Assessment

• 2024/2025 2nd module
  0.2 * Контрольная + 0.8 * Экзамен

Bibliography

Recommended Core Bibliography

• Dynamical Systems : Stability, Symbolic Dynamics, and Chaos, 2nd ed., 504 p., Robinson, C., 1999
• Dynamical Systems on 2- and 3-Manifolds, XXVI, 295 p., Grines, V. Z., Medvedev, T. V., Pochinka, O. V., 2016
• Introduction to the Modern Theory of Dynamical Systems, With a supplement by Anatole Katok and Leonardo Mendoza, XVIII, 802 p., Katok, A., Hasselblatt, B., 1996

Recommended Additional Bibliography

• Differentiable Dynamical Systems : An Introduction to Structural Stability and Hyperbolicity, XI, 192 p., Wen, L., 2016
• Iteration of Rational Functions : Complex Analytic Dynamical Systems, XVI, 280 p., Beardon, A. F., 2000

Authors

• Nozdrinova Elena Viacheslavovna
• Zhuzhoma Evgenii Viktorovich