Geodesic
The skew product on $n$-dimensional cell with transitive but not totally transitive $n$-dimensional attractor
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2016), pp. 91-100.

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We construct an example of the skew product on the $n$-dimensional cell with the transitive but not totally transitive $n$-dimensional attractor.
Keywords: topological transitivity, attractor. 
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A. S. Fil'chenkov. The skew product on $n$-dimensional cell with transitive but not totally transitive $n$-dimensional attractor. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2016), pp. 91-100. http://geodesic.mathdoc.fr/item/IVM_2016_6_a9/

[1] Anischenko V. S., Astakhov V. V., Vadivasova T. E., Neiman A. B., Strelkova G. I., Shimanskii-Gaier L., Nelineinye effekty v khaoticheskikh i stokhasticheskikh sistemakh, In-t kompyuternykh issledov., Moskva–Izhevsk, 2003

[2] Efremova L. S., “Example of the smooth skew product in the plane with the one-dimensional ramified continuum as the global attractor”, ESAIM: Proceedings, 36 (2012), 15–24 | DOI | MR

[3] Efremova L. S., “Differentsialnye svoistva i prityagivayuschie mnozhestva prosteishego kosogo proizvedeniya otobrazhenii intervala”, Matem. sb., 201:6 (2010), 93–130 | DOI | MR | Zbl

[4] Volk D., “Persistent massive attractors of smooth maps”, Ergodic Theory and Dynamical Systems, 34:2 (2014), 693–704 | DOI | MR | Zbl

[5] Viana M., “Multidimensional nonhyperbolic attractors”, Publ. Math. de L'IHES, 85:1 (1997), 63–96 | DOI | MR | Zbl

[6] Bamon R., Kiwi J., Rivera-Letelier J., Urzua R., “On the topology of solenoidal attractors of the cylinder”, Annales de l'Institut Henri Poincaré. Nonlinear Anal., 23:2 (2006), 209–236 | DOI | MR | Zbl

[7] de Melo W., van Strien S., One-dimensional dynamics, Springer, 1996

[8] Katok A., Khasselblat B., Vvedenie v sovremennuyu teoriyu dinamicheskikh sistem, Faktorial, M., 1999

[9] Alseda Ll., Del Rio M. A., Rodriguez J. A., “A survey on the relation between transitivity and dense periodicity for graph maps”, JDEA, 9:3–4 (2003), 281–288 | MR | Zbl

[10] Efremova L. S., Fil'chenkov A. S., “Boundary conditions for maps in fibers and topological transitivity of skew products of interval maps”, J. Math. Sci. (NY), 208:1 (2015), 109–114 | DOI | MR | Zbl

[11] Dyakonov V. P., Entsiklopediya kompyuternoi algebry, DMK-Press, M., 2009

[12] Sharkovskii A. N., Maistrenko Yu. L., Romanenko E. Yu., Raznostnye uravneniya i ikh prilozheniya, Nauk. dumka, Kiev, 1986 | MR

[13] Kurosh A. G., Kurs vysshei algebry, Nauka, M., 1968

[14] Zorich V. A., Matematicheskii analiz, Fazis, M., 1997 | MR

[15] Brur Kh. V., Dyumorte F., van Strin S., Takens F., Struktury v dinamike, In-t kompyuternykh issledov., Moskva–Izhevsk, 2003

[16] Devaney R., An introduction to chaotic dynamical systems, Addison-Wesley, 1989 | MR | Zbl

[17] Banks J., Brooks J., Cairns G., Davis G., Stacey P., “On Devaney's definition of chaos”, The Amer. Math. Monthly, 99:4 (1992), 332–334 | DOI | MR | Zbl