Cone criterion on an~infinite-dimensional torus
Izvestiya. Mathematics , Tome 88 (2024) no. 6, pp. 1087-1118
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On the infinite-dimensional torus
$\mathbb{T}^{\infty} = E/2\pi\mathbb{Z}^{\infty}$,
where $E$ is an infinite-dimensional real Banach space,
$\mathbb{Z}^{\infty}$is an abstract integer lattice, a special class
of diffeomorphisms $\mathrm{Diff}(\mathbb{T}^{\infty})$ is considered.
This class consists of the mappings
$G\colon \mathbb{T}^{\infty} \to \mathbb{T}^{\infty}$
such that the differentials $DG$ and $D(G^{-1})$
are uniformly bounded and uniformly continuous on $\mathbb{T}^{\infty}$.
For diffeomorphisms from $\mathrm{Diff}(\mathbb{T}^{\infty})$, we establish
the validity of the so-called cone criterion, which is a classical result
of finite-dimensional hyperbolic theory (that is, the hyperbolicity criterion
formulated in terms of fields of invariant horizontal and vertical cones).
Keywords:
infinite-dimensional torus, diffeomorphism, hyperbolicity, cone criterion.
@article{IM2_2024_88_6_a3,
author = {S. D. Glyzin and A. Yu. Kolesov},
title = {Cone criterion on an~infinite-dimensional torus},
journal = {Izvestiya. Mathematics },
pages = {1087--1118},
publisher = {mathdoc},
volume = {88},
number = {6},
year = {2024},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_2024_88_6_a3/}
}
S. D. Glyzin; A. Yu. Kolesov. Cone criterion on an~infinite-dimensional torus. Izvestiya. Mathematics , Tome 88 (2024) no. 6, pp. 1087-1118. http://geodesic.mathdoc.fr/item/IM2_2024_88_6_a3/