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Hyperbolic Attractors Which are Anosov Tori
Marina K. Barinova, Vyacheslav Z. Grines, Olga V. Pochinka, Evgeny V. Zhuzhoma HSE University,
ul. Bolshaya Pecherckaya 25/12, 603155 Nizhny Novgorod, Russia
Аннотация:
We consider a topologically mixing hyperbolic attractor $\Lambda\subset M^n$ for a diffeomorphism $f:M^n\to M^n$ of a compact orientable $n$-manifold $M^n$, $n>3$. Such an attractor $\Lambda$ is called an Anosov torus provided the restriction $f|_{\Lambda}$ is conjugate to Anosov algebraic automorphism of $k$-dimensional torus $\mathbb T^k$.
We prove that $\Lambda$ is an Anosov torus for two cases:
1) $\dim{\Lambda}=n-1$, $\dim{W^u_x}=1$, $x\in\Lambda$;
2) $\dim\,\Lambda=k,\,\dim\, W^u_x=k-1,\,x\in\Lambda$, and $\Lambda$ belongs to an $f$-invariant closed $k$-manifold, $2\leqslant k\leqslant n$, topologically embedded in $M^n$.
Ключевые слова:
hyperbolic attractor, Anosov diffeomorphism, $\Omega$-stable diffeomorphism, chaotic attractor
Поступила в редакцию: 18.05.2023 Принята в печать: 25.10.2023
Образец цитирования:
Marina K. Barinova, Vyacheslav Z. Grines, Olga V. Pochinka, Evgeny V. Zhuzhoma, “Hyperbolic Attractors Which are Anosov Tori”, Regul. Chaotic Dyn., 29:2 (2024), 369–375
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd1259 https://www.mathnet.ru/rus/rcd/v29/i2/p369
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