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=== Bifurcations ===
* [http://www.dyn-sys.org/w/images/3/35/CHA20-AR-GBC2021-01328.pdf "Germs of bifurcation diagrams and SN-SN families"]  by Yu. Ilyashenko, Chaos 31, 1, 2021, [https://doi.org/10.1063/5.0030742  https://doi.org/10.1063/5.0030742]
* Papers on global bifurcations in one-parameter families:
[http://www.dyn-sys.org/w/images/8/8c/Starichkova_tame_1_par_families.pdf "Global bifurcations in generic one-parameter families on S^2" by V. Starichkova.]
[http://www.dyn-sys.org/w/images/a/a6/IS_saddle_loop.pdf "Global bifurcations in generic one-parameter families with a separatrix loop on S^2" by Yu. Ilyashenko and N. Solodovnikov.]
[http://www.dyn-sys.org/w/images/5/5e/GIS_parabolic_cycle.pdf "Global bifurcations in generic one-parameter families with a parabolic cycle on S^2" by N. Goncharuk, Yu. Ilyashenko, and N. Solodovnikov.]    [https://arxiv.org/pdf/1707.09779.pdf (arXiv:1707.09779)]
=== Foliations ===  
=== Foliations ===  
* Alexey Glutsyuk and Mikhail Lyubich. [http://wiki.dynsys.org/misc/uerghyp.pdf Unique ergodicity of horospheric foliations revisited].
* Alexey Glutsyuk and Mikhail Lyubich. [http://wiki.dynsys.org/misc/uerghyp.pdf Unique ergodicity of horospheric foliations revisited].
* B. Deroin, V. Kleptsyn, [http://arxiv.org/abs/math/0506204 Random conformal dynamical systems], ''Geometry and Functional Analysis'', '''17''' (2007), no. 4, pp. 1043-1105.
* B. Deroin, V. Kleptsyn, [http://arxiv.org/abs/math/0506204 Random conformal dynamical systems], ''Geometry and Functional Analysis'', '''17''' (2007), no. 4, pp. 1043-1105.
==== Foliations in <math>\mathbb{C}^2</math> ====
===== Foliations in complex plane =====
* D. Volk, [http://dx.doi.org/10.1134%2FS0081543806030072 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.: [http://denisvolk.com/math/ru/papers/seplink.pdf 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)
* D. Volk, [http://dx.doi.org/10.1134%2FS0081543806030072 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.: [http://denisvolk.com/math/ru/papers/seplink.pdf 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.
* 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 ===
=== Attractors & time averages ===
==== Invisible attractors ====
===== Thick attractors =====
* Yu. Ilyashenko, A. Negut, [http://wiki.dynsys.org/misc/NON-IN-final.pdf Invisible parts of attractors]. Nonlinearity '''23''' (2010) 1199—1219. [http://stacks.iop.org/Non/23/1199]
* Yu. Ilyashenko, Thick Attractors of Step Skew Products, ''Regular and Chaotic Dynamics'', Vol. '''15''', Nos. 2-3, pp. 328-334
* Yu. Ilyashenko, D. Volk, [http://denisvolk.com/math/en/papers/cascad_edit.pdf Cascades of <math>\varepsilon</math>-invisibility], Journal of Fixed Point Theory and Applications, 2010, 7, 161--188 (Рус.: [http://denisvolk.com/math/ru/papers/cascad_rus.pdf Каскады <math>\varepsilon</math>-невидимости])
 
==== Other examples of pathological attractors ====
* D. Volk, [http://arxiv.org/abs/1108.5330 Persistent massive attractors of smooth maps], arXiv:1108.5330
 
===== Invisible attractors =====
* Yu. Ilyashenko, A. Negut, [http://dyn-sys.org/misc/NON-IN-final.pdf Invisible parts of attractors]. ''Nonlinearity'', '''23''' (2010) 1199—1219. [http://stacks.iop.org/Non/23/1199]
* Yu. Ilyashenko, D. Volk, [http://denisvolk.com/math/en/papers/cascad_edit.pdf Cascades of <math>\varepsilon</math>-invisibility], ''Journal of Fixed Point Theory and Applications'', '''7''', 2010, 161--188 (Рус.: [http://denisvolk.com/math/ru/papers/cascad_rus.pdf 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.
* 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.
* 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 ====
===== 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.
* 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, [http://arxiv.org/abs/1109.4060 Special Ergodic Theorem for hyperbolic maps], arXiv:1109.4060


=== Lyapunov exponents ===
=== Lyapunov exponents ===
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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)]
* I. V. Schurov. ''Canard cycles in generic slow-fast systems on the two-torus.'' To appear in ”Transactions of the Moscow Mathematical Society”, accepted in 2009. (Рус.: ''Уточные циклы в типичных быстро-медленных системах на торе.'')
* 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
* I. V. Schurov. [http://www.dyn-sys.org/public/ducks-on-torus-nonconvex-AIMS.pdf ''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.
** 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)].


=== Limit cycles ===
=== 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. [http://www.dyn-sys.org/public/kaleda-schurov-HA.pdf  «Цикличность элементарных полициклов с фиксированным числом особых точек в типичных k-параметрических семействах»]. Алгебра и анализ. '''22''':4 (2010), 57—75)
* 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. [http://www.dyn-sys.org/public/kaleda-schurov-HA.pdf  «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. [http://www.dyn-sys.org/files/bill-jmd.pdf "No planar billiard possesses an open set of quadrilateral trajectories"], submitted to [http://www.math.psu.edu/jmd/ Journal of Modern Dynamics].

Текущая версия от 06:10, 5 января 2021


Bifurcations

"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

Foliations in complex plane

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
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


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

Slow-fast systems

Limit cycles

Periodic orbits

Источник — http://www.dyn-sys.org/w/index.php?title=Papers&oldid=2432