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=== Slow-fast systems === | === Slow-fast systems === | ||
* I. V. Schurov. [http://dx.doi.org/10.1007/s10883-010-9093-9 ''Ducks On The Torus: Existence and Uniqueness'']. Journal of Dynamical and Control Systems, '''16''':2 (2010), 267—300. Preprint: [http://arxiv.org/abs/0910.1888 arXiv:0910.1888v1 (math.DS)] | * I. V. Schurov. [http://dx.doi.org/10.1007/s10883-010-9093-9 ''Ducks On The Torus: Existence and Uniqueness'']. Journal of Dynamical and Control Systems, '''16''':2 (2010), 267—300. Preprint: [http://arxiv.org/abs/0910.1888 arXiv:0910.1888v1 (math.DS)] | ||
* | * Щуров И.В. [http://dyn-sys.org/public/ducks-nonconvex-trudy.pdf ''Уточные циклы в типичных быстро-медленных системах на торе.''], Труды ММО '''71''' (2010), 200-234 | ||
** Translation: I. V. Shchurov. ''[http://www.ams.org/journals/mosc/2010-71-00/S0077-1554-2010-00184-7/home.html Canard cycles in generic fast-slow systems on the torus.]'' Transactions of the Moscow Mathematical Society, '''2010''', 175-207 [http://www.dyn-sys.org/public/ducks-nonconvex-trudy-en.pdf 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, [http://arxiv.org/abs/1008.0133 arXiv:1008.0133 (Math.DS)]. | * 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, [http://arxiv.org/abs/1008.0133 arXiv:1008.0133 (Math.DS)]. | ||
Версия от 15:09, 7 марта 2011
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
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.
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.
