Papers

Bifurcations

• "Germs of bifurcation diagrams and SN-SN families" by Yu. Ilyashenko, Chaos 31, 1, 2021, https://doi.org/10.1063/5.0030742
• Papers on global bifurcations in one-parameter families:

"Global bifurcations in generic one-parameter families on S^2" by V. Starichkova.

"Global bifurcations in generic one-parameter families with a separatrix loop on S^2" by Yu. Ilyashenko and N. Solodovnikov.

"Global bifurcations in generic one-parameter families with a parabolic cycle on S^2" by N. Goncharuk, Yu. Ilyashenko, and N. Solodovnikov. (arXiv:1707.09779)

Foliations

• Alexey Glutsyuk and Mikhail Lyubich. Unique ergodicity of horospheric foliations revisited.
• B. Deroin, V. Kleptsyn, Random conformal dynamical systems, Geometry and Functional Analysis, 17 (2007), no. 4, pp. 1043-1105.

Foliations in complex plane

• D. Volk, The density of separatrix connections in the space of polynomial foliations in <math>\mathbb{C}P^2</math>, Proceedings of the Steklov Institute of Mathematics (2006), vol. 254, pp. 169-179 (Рус.: Плотность сепаратрисных связок в пространстве полиномиальных слоений в <math>\mathbb{C}P^2</math>, Нелинейные аналитические дифференциальные уравнения, Сборник статей, Тр. МИАН, 254, Наука, М., 2006, 181–191)
• T. Golenishcheva-Kutuzova, V. Kleptsyn, Minimality and ergodicity of a generic analytic foliation of <math>\mathbb{C}^2</math>, Ergodic Theory and Dynamical Systems, 28 (2008), no. 5, pp. 1533--1544.

Attractors & time averages

Thick attractors

• Yu. Ilyashenko, Thick Attractors of Step Skew Products, Regular and Chaotic Dynamics, Vol. 15, Nos. 2-3, pp. 328-334

• D. Volk, Persistent massive attractors of smooth maps, arXiv:1108.5330

Invisible attractors

• Yu. Ilyashenko, A. Negut, Invisible parts of attractors. Nonlinearity, 23 (2010) 1199—1219. [1]
• Yu. Ilyashenko, D. Volk, Cascades of <math>\varepsilon</math>-invisibility, Journal of Fixed Point Theory and Applications, 7, 2010, 161--188 (Рус.: Каскады <math>\varepsilon</math>-невидимости)

Other examples of pathological attractors

• V. Kleptsyn, An example of non-coincidence of minimal and statistical attractors, Ergodic Theory and Dynamical Systems, 26 (2006), no. 3, pp. 759-768.
• T. Golenishcheva-Kutuzova, V. Kleptsyn, Non-convergence of the Krylov-Bogolubov procedure for the Bowen's example, Mathematical Notes, 82 (2007), no. 5, pp. 678—689.

Ittai Kan example

• Yu. Ilyashenko, V. Kleptsyn, P. Saltykov, Openness of the set of boundary preserving maps of an annulus with intermingled attracting basins. Journal of Fixed Point Theory and Applications, 3 (2008), no. 2, pp. 449--463.

Special Ergodic Theorem

• V. Kleptsyn, D. Ryzhov, Special Ergodic Theorem for hyperbolic maps, arXiv:1109.4060

Lyapunov exponents

• A. S. Gorodetski, Yu. S. Ilyashenko, V. A. Kleptsyn, M. B. Nalsky, Nonremovable Zero Lyapunov Exponents, Funkts. Anal. Prilozh., 39:1 (2005), 27–38
• V. Kleptsyn, M. Nalski, Stability of existence of non-hyperbolic measures for C¹-diffeomorphisms, Functional Analysis and its Applications, 41 (2007), no. 4, pp. 271--283.

One-dimensional dynamics

• B. Deroin, V. Kleptsyn, A. Navas, Sur la dynamique unidimensionelle et régularité intermédiaire, preprint IHES M/05/24, Acta Mathematica, 199 (2007), pp. 199--262.
• V. Kleptsyn, A. Navas, A Denjoy type theorem for commuting circle diffeomorphisms with derivatives having different Hölder differentiability classes, Moscow Math. Journal 8 (2008), no. 3, 477-492, 616.
• B. Deroin, V. Kleptsyn, A. Navas, On the question of ergodicity for minimal group actions on the circle, Moscow Math. Journal, 9 (2009), no. 2, pp. 263--303.

Slow-fast systems

• I. V. Schurov. Ducks On The Torus: Existence and Uniqueness. Journal of Dynamical and Control Systems, 16:2 (2010), 267—300. Preprint: arXiv:0910.1888v1 (math.DS)
• Щуров И.В. Уточные циклы в типичных быстро-медленных системах на торе., Труды ММО 71 (2010), 200-234
  • Translation: I. V. Shchurov. Canard cycles in generic fast-slow systems on the torus. Transactions of the Moscow Mathematical Society, 2010, 175-207 PDF
• I. V. Schurov. Duck farming on the two-torus: multiple canard cycles in generic slow-fast systems, submitted to the proceedings for the Eighth AIMS International Conference on Dynamical Systems, Differential Equations and Applications, arXiv:1008.0133 (Math.DS).

Limit cycles

• P. Kaleda, I. Schurov. Cyclicity of Elementary Polycycles with Fixed Singular Points Number in Generic k-Parametric Families. Algebra and Analysis (St. Petersburg Mathematical Journal) (Рус.: П. И. Каледа, И. В. Щуров. «Цикличность элементарных полициклов с фиксированным числом особых точек в типичных k-параметрических семействах». Алгебра и анализ. 22:4 (2010), 57—75)

Periodic orbits

• A. Glutsyk, Yu. Kudryashov. "No planar billiard possesses an open set of quadrilateral trajectories", submitted to Journal of Modern Dynamics.