. "000285265100019" . "12"^^ . "19" . . "RIV/61988987:17610/10:A1100RIW" . "P(1M0572), Z(MSM4781305904)" . . . "3-4" . . "3"^^ . . "On the $\\omega$-limit sets of product maps"@en . "[5911BFE0B0F9]" . . . "276894" . "Jim\u00E9nez L\u00F3pez, Victor" . . "17610" . . . "1"^^ . "Let $\\omega(\\cdot)$ denote the union of all $\\omega$-limit sets of a given map. As the main result of this paper we prove that, for given continuous interval maps $f_1,\\ldots, f_m$, the set of $\\omega$-limit points of the product map $f_1 \\times \\cdots \\times f_m$ and the cartesian product of the sets $\\omega(f_1),\\ldots, \\omega(f_m)$ coincide. This result substantially enriches the theory of multidimensional permutation product maps, i.e., maps of the form $F(x_1,\\ldots, x_m) = (f_{\\sigma(1)}(x_{\\sigma(1)}), \\ldots,f_{\\sigma(m)}(x_{\\sigma(m)}))$, where $\\sigma$ is a permutation of the set of indices $\\{1,\\ldots,m\\}$. Especially, for any such map $F$, we prove that the set $\\omega(F)$ is closed and we also show that $\\omega(F)$ cannot be a proper subset of the center of the map $F$. These results solve open questions mentioned, e.g., in [F. Balibrea, J. S. C\\'{a}novas, A. Linero, {\\em New results on topological dynamics of antitriangular maps\\/}, Appl. Gen. Topol.]."@en . "Kupka, Ji\u0159\u00ED" . . . "1056-2176" . "Discrete dynamical system; interval map; product map; permutation product map; antitriangular map; $\\omega$-limit set; solenoidal set; basic set; center"@en . . . . . . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . "Linero, Antonio" . . "Let $\\omega(\\cdot)$ denote the union of all $\\omega$-limit sets of a given map. As the main result of this paper we prove that, for given continuous interval maps $f_1,\\ldots, f_m$, the set of $\\omega$-limit points of the product map $f_1 \\times \\cdots \\times f_m$ and the cartesian product of the sets $\\omega(f_1),\\ldots, \\omega(f_m)$ coincide. This result substantially enriches the theory of multidimensional permutation product maps, i.e., maps of the form $F(x_1,\\ldots, x_m) = (f_{\\sigma(1)}(x_{\\sigma(1)}), \\ldots,f_{\\sigma(m)}(x_{\\sigma(m)}))$, where $\\sigma$ is a permutation of the set of indices $\\{1,\\ldots,m\\}$. Especially, for any such map $F$, we prove that the set $\\omega(F)$ is closed and we also show that $\\omega(F)$ cannot be a proper subset of the center of the map $F$. These results solve open questions mentioned, e.g., in [F. Balibrea, J. S. C\\'{a}novas, A. Linero, {\\em New results on topological dynamics of antitriangular maps\\/}, Appl. Gen. Topol.]." . . . "On the $\\omega$-limit sets of product maps" . . "On the $\\omega$-limit sets of product maps"@en . "Dynamic Systems and Applications" . . "RIV/61988987:17610/10:A1100RIW!RIV11-MSM-17610___" . "On the $\\omega$-limit sets of product maps" .