Education and Science

Candidate of Sciences in Applied Mathematics

2024

Degree Awarded: By decision of the dissertation council, the academic degree of Candidate of Sciences in Applied Mathematics was awarded (Protocol No. 29 dated 30.09.2024)

Dissertation Topic: On chaotic attractors and repellers in systems with a compact phase space

Summary: The dissertation is dedicated to the study of chaotic dynamics in systems described by diffeomorphisms on compact manifolds. New methods for analyzing chaotic dynamics have been developed, including determining the applicability limits of linear response theory and verifying the non-uniform hyperbolicity of a system. A novel scenario of attractor–repeller collision for three-dimensional torus maps has been demonstrated, along with methods for constructing heterodimensional cycles. A software package for studying reversible and dissipative systems has been created. The results have been presented at international conferences and seminars and published in leading journals on dynamical chaos theory.

Scientific Advisor: Alexey O. Kazakov

PhD Studies

2020-2023

During PhD studies:

  • Three papers were published in leading journal on dynamical chaos theory and its applications.
  • Completed an internship at the University of Potsdam under the supervision of Prof. A. Pikovsky.
  • Delivered presentations at international seminars and conferences.
  • Passed exams in a foreign language, philosophy, science methodology, and the state exam.
  • Completed teaching practice: conducted programming classes for first-year students for three years.

Publications

Tools and Software Development

In research, Python and C were actively used for numerical experiments. Key tools:

  • NumPy – working with numerical arrays;
  • Matplotlib – data visualization;
  • c2dll – a custom library for convenient function calls from C in Python, significantly accelerating computationally intensive algorithms.

The developed software package allows:

  • calculating the Kantorovich-Rubinstein-Wasserstein distance between an attractor and a repeller;
  • computing the relative Rényi dimensions and mutual singularities of an attractor and a repeller;
  • constructing heterodimensional cycles for three-dimensional systems demonstating attractor–repeller intersections.

Higher Education

2004-2009

University: Lobachevsky State University of Nizhny Novgorod
Faculty: Faculty of Computational Mathematics and Cybernetics
Major: Applied Informatics
Specialization: Mathematical Software of Computers

Thesis Project: Subsystem for Conducting Mass Experiments and Optimizing Extended Precision Arithmetic in the Global Expert Software Package

Professional Profiles