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.

Full 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

kontrol work
exam

Interim Assessment

2022/2023 2nd module
0.3 * kontrol work + 0.7 * exam

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

Master’s Programme 'Mathematics'

Contacts

Dynamics of endomorphism