Yu. G. Kudryashov, “Bony Attractors”, Funktsional. Anal. i Prilozhen., 44:3 (2010), 73–76; Funct. Anal. Appl., 44:3 (2010), 219

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Funktsional'nyi Analiz i ego Prilozheniya, 2010, Volume 44, Issue 3, Pages 73–76
DOI: https://doi.org/10.4213/faa2997 (Mi faa2997)

This article is cited in 20 scientific papers (total in 20 papers)

Brief communications

Bony Attractors

Yu. G. Kudryashov^abc

^a M. V. Lomonosov Moscow State University
^b Independent University of Moscow
^c Ecolé Normale Supériore de Lyon

Full-text PDF (153 kB) Citations (20)

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DOI: https://doi.org/10.4213/faa2997

Abstract: A new possible geometry of an attractor of a dynamical system, a bony attractor, is described. A bony attractor is the union of two parts. The first part is the graph of a continuous function defined on a subset of

$\Sigma^k$ , the set of bi-infinite sequences of integers

$m$ in the range

$0\le m<k$ . The second part is the union of uncountably many intervals contained in the closure of the graph. An open set of skew products over the Bernoulli shift

$(\sigma\omega)_i=\omega_{i+1}$ with fiber

$[0,1]$ is constructed such that each system in this set has a bony attractor.

Keywords: attractor, dynamical system, skew product, Bernoulli shift.

Received: 13.07.2009

English version:
Functional Analysis and Its Applications, 2010, Volume 44, Issue 3, Pages 219–222
DOI: https://doi.org/10.1007/s10688-010-0028-8

Bibliographic databases:

Document Type: Article

UDC: 517.938

Language: Russian

Citation: Yu. G. Kudryashov, “Bony Attractors”, Funktsional. Anal. i Prilozhen., 44:3 (2010), 73–76; Funct. Anal. Appl., 44:3 (2010), 219–222

Citation in format AMSBIB

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https://doi.org/10.4213/faa2997

https://www.mathnet.ru/eng/faa/v44/i3/p73

This publication is cited in the following 20 articles:

Lorenzo J. Díaz, Katrin Gelfert, Michał Rams, “Mingled hyperbolicities: Ergodic properties and bifurcation phenomena (an approach using concavity)”, DCDS, 42:11 (2022), 5309
Pablo G. Barrientos, Yushi Nakano, Artem Raibekas, Mario Roldan, “Topological entropy and Hausdorff dimension of irregular sets for non-hyperbolic dynamical systems”, Dynamical Systems, 37:2 (2022), 181
Matias E. Silva E., “Random Iterations of Maps on Rk: Asymptotic Stability, Synchronisation and Functional Central Limit Theorem”, Nonlinearity, 34:3 (2021), 1577–1597
Lorenzo J. Díaz, Edgar Matias, “Attracting graphs of skew products with non-contracting fiber maps”, Math. Z., 291:3-4 (2019), 1543
M. Zaj, F. H. Ghane, “Non Hyperbolic Solenoidal Thick Bony Attractors”, Qual. Theory Dyn. Syst., 18:1 (2019), 35
Walkden C.P., Withers T., “Invariant Graphs of a Family of Non-Uniformly Expanding Skew Products Over Markov Maps”, Nonlinearity, 31:6 (2018), 2726–2755
Lorenzo J Díaz, Edgar Matias, “Stability of the Markov operator and synchronization of Markovian random products”, Nonlinearity, 31:5 (2018), 1782
Ilyashenko Yu. Shilin I., “Attractors and Skew Products”, Modern Theory of Dynamical Systems: a Tribute to Dmitry Victorovich Anosov, Contemporary Mathematics, 692, ed. Katok A. Pesin Y. Hertz F., Amer Mathematical Soc, 2017, 155–175
Malicet D., “Random Walks on Homeo(S (1))”, Commun. Math. Phys., 356:3 (2017), 1083–1116
Okunev A., “Milnor Attractors of Skew Products With the Fiber a Circle”, J. Dyn. Control Syst., 23:2 (2017), 421–433
Gharaei M., Homburg A.J., “Skew products of interval maps over subshifts”, J. Differ. Equ. Appl., 22:7 (2016), 941–958
Yulij Ilyashenko, Olga Romaskevich, “Sternberg Linearization Theorem for Skew Products”, J Dyn Control Syst, 22:3 (2016), 595
Diaz L.J., Marcarini T., “Generation of Spines in Porcupine-Like Horseshoes”, Nonlinearity, 28:11 (2015), 4249–4279
V. Kleptsyn, D. Volk, “Physical measures for nonlinear random walks on interval”, Mosc. Math. J., 14:2 (2014), 339–365
L J Díaz, K Gelfert, M Rams, “Abundant rich phase transitions in step-skew products”, Nonlinearity, 27:9 (2014), 2255
Diaz L.J. Gelfert K., “Porcupine-Like Horseshoes: Topological and Ergodic Aspects”, Progress and Challenges in Dynamical Systems, Springer Proceedings in Mathematics & Statistics, 54, ed. Ibanez S. DelRio J. Pumarino A. Rodriguez J., Springer-Verlag Berlin, 2013, 199–219
Yu. S. Ilyashenko, I. S. Shilin, “Relatively unstable attractors”, Proc. Steklov Inst. Math., 277 (2012), 84–93
Yu. S. Ilyashenko, “Multidimensional Bony Attractors”, Funct. Anal. Appl., 46:4 (2012), 239–248
Ilyashenko Yu. Negut A., “Hölder properties of perturbed skew products and Fubini regained”, Nonlinearity, 25:8 (2012), 2377–2399
Diaz L.J. Gelfert K., “Porcupine-like horseshoes: transitivity, Lyapunov spectrum, and phase transitions”, Fund. Math., 216:1 (2012), 55–100

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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