Alexander Krasnoselskii
- Department Head, Professor:Faculty of Mathematics / Joint Department with the Kharkevich Institute for Information Transmission Problems (RAS)
- Alexander Krasnoselskii has been at HSE University since 2008.
Education, Degrees and Academic Titles
- 1992Senior Research Fellow
- 1989
Doctor of Sciences* in Differential Equations, Dynamic Systems and Optimal Control
Institute for Systems Studies of the Russian Academy of Sciences - 1981
Candidate of Sciences* (PhD)
- 1976
Degree
Lomonosov Moscow State University
According to the International Standard Classification of Education (ISCED) 2011, Candidate of Sciences belongs to ISCED level 8 - "doctoral or equivalent", together with PhD, DPhil, D.Lit, D.Sc, LL.D, Doctorate or similar. Candidate of Sciences allows its holders to reach the level of the Associate Professor.
A post-doctoral degree called Doctor of Sciences is given to reflect second advanced research qualifications or higher doctorates in ISCED 2011.
Research interests
Nonlinear analysis in various directions: nonlinear boundary value problems for differential equations, dynamic sytems, bifurcations (Hopf bifurcations, bifurcatrions at infinity), degenerate systems,control theory, hysteresis phenomenon, systems with hysteresis, asynchronous systems, numerical methods
Courses (2023/2024)
- Academic Mentor's Seminar "Analysis, Dynamical Systems and Probability Theory" (Master’s programme; Faculty of Mathematics; 2 year, 1-4 module)Eng
- Past Courses
Courses (2022/2023)
- Academic Mentor's Seminar "Analysis, Dynamical Systems and Probability Theory" (Master’s programme; Faculty of Mathematics; 1 year, 1-4 module)Eng
- Differential Equations (Bachelor’s programme; Faculty of Physics; 1 year, 3, 4 module)Rus
Fourier Analysis (Bachelor’s programme; Faculty of Mathematics; field of study "01.03.01. Математика", field of study "01.03.01. Математика"; 2 year, 3, 4 module)Rus
Courses (2021/2022)
Calculus (Bachelor’s programme; Faculty of Mathematics; field of study "01.03.01. Математика", field of study "01.03.01. Математика"; 2 year, 1-4 module)Rus
Courses (2020/2021)
Calculus (Bachelor’s programme; Faculty of Mathematics; field of study "01.03.01. Математика", field of study "01.03.01. Математика"; 1 year, 1-4 module)Rus
Courses (2019/2020)
Calculus (Bachelor’s programme; Faculty of Mathematics; field of study "01.03.01. Математика", field of study "01.03.01. Математика"; 2 year, 1-4 module)Rus
Courses (2018/2019)
Calculus (Bachelor’s programme; Faculty of Mathematics; field of study "01.03.01. Математика", field of study "01.03.01. Математика"; 1 year, 1-4 module)Rus
- Mathematics. Licenciatus (Bachelor’s programme; Faculty of Mathematics; 3 year, 4 module)Rus
- Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
Courses (2017/2018)
- Calculus (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
- Functional Analysis 1 (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Eng
- Mathematical Practical Training 2 (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
- Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
Editorial board membership
2004: Member of the Editorial Board, Автоматика и телемеханика (Automation and Remote Control).
Publications12
- Article Krasnoselskii A., Kloeden P., Rachinskii D. I., Krejci P. Alexei V. Pokrovskii (02.06.1948 -- 01.09.2010) // Discrete and Continuous Dynamical Systems - Series B. 2013. Vol. 18. No. 2. P. i-iii.
- Article Krasnosel'skii Alexander M., O'Grady E., Pokrovskii A., Rachinskii D. I. Periodic canard trajectories with multiple segments following the unstable part of critical manifold // Discrete and Continuous Dynamical Systems - Series B. 2013. Vol. 18. No. 2. P. 467-482. doi
- Article Krasnosel'skii Alexander M. Resonant forced oscillations in systems with periodic nonlinearities // Discrete and Continuous Dynamical Systems. 2013. Vol. 33. No. 1. P. 239-254.
- Article Alexander M. Krasnosel’skii. Unbounded sequences of cycles in general autonomous equations with periodic nonlinearities // Discrete and Continuous Dynamical Systems - Series S. 2013. Vol. 6. No. 4. P. 999-1016. doi
- Article Красносельский А. М. Системы с периодическими нелинейностями // Доклады Академии наук. 2011. Т. 438. № 2. С. 176-180.
- Article Krasnoselskii A. Index at infinity and bifurcations of twice degenerate vector fields // Topological Methods in Nonlinear Analysis. 2010. Vol. 35. No. 1. P. 99-126.
- Article Красносельский А. М. Неограниченные ветви вынужденных колебаний // Дифференциальные уравнения. 2009. Т. 45. № 3. С. 334-353.
- Article Kozyakin V., Krasnoselskii A., Rachinskii D. Arnold tongues for bifurcation from infinity // Discrete and Continuous Dynamical Systems - Series S. 2008. Vol. 1. No. 1. P. 107-116.
- Article Kozyakin V., Krasnoselskii A., Rachinskii D. Asymptotics of Arnold tongues in problems at infinity // Discrete and Continuous Dynamical Systems. 2008. Vol. 20. No. 4. P. 989-1011.
- Article Красносельский А. М. Двойное вырождение в задаче о неограниченных ветвях вынужденных колебаний // Доклады Академии наук. 2008. Т. 419. № 1. С. 14-18.
- Article Красносельский А. М., Рачинский Д. Критерии возникновения нелинейного резонанса в одноконтурной системе управления с насыщением // Автоматика и телемеханика. 2008. № 8. С. 33-47.
- Article Красносельский А. М., Рачинский Д. О несвязных неограниченных множествах вынужденных колебаний // Доклады Академии наук. 2008. Т. 422. № 1. С. 21-25.