"375 ; 401" . "level set of a map on compact manifold; topological entropy"@en . "27"^^ . . "Topoligick\u00E1 entropie m-n\u00E1sobn\u00FDch zobrazen\u00ED"@cs . "0143-3857" . "We investigate the relation between preimage multiplicity and topological entropy for continuous maps. An argument originated by Misiurewicz and Przytycki shows that if every regular value of a $C^{1}$ map has at least $m$ preimages then the topological entropy of the map is at least $\\log m$. For every integer, there exist continuous maps of the circle with entropy zero for which every point has at least $m$ preimages. We show that if in addition there is a positive uniform lower bound on the diameter of all pointwise preimage sets, then the entropy is at least $\\log m$." . "1"^^ . . "21110" . . "Nitecki, Z." . "Topological Entropy of m-fold Maps"@en . "We investigate the relation between preimage multiplicity and topological entropy for continuous maps. An argument originated by Misiurewicz and Przytycki shows that if every regular value of a $C^{1}$ map has at least $m$ preimages then the topological entropy of the map is at least $\\log m$. For every integer, there exist continuous maps of the circle with entropy zero for which every point has at least $m$ preimages. We show that if in addition there is a positive uniform lower bound on the diameter of all pointwise preimage sets, then the entropy is at least $\\log m$."@en . . . "Bobok, Jozef" . "546921" . . "2"^^ . . "Topological Entropy of m-fold Maps" . "RIV/68407700:21110/05:01117873" . "Topological Entropy of m-fold Maps" . . "V \u010Dl\u00E1nku je vy\u0161et\u0159ov\u00E1na z\u00E1vislost topologick\u00E9 entropie a po\u010Dtu prvk\u016F \u00FArov\u0148ov\u00FDch mno\u017Ein C^1-zobrazen\u00ED kompaktn\u00ED variety do sebe. Pro kru\u017Enici jsou dok\u00E1z\u00E1ny v\u00FDsledky bez p\u0159edpokladu hladkosti."@cs . . . "RIV/68407700:21110/05:01117873!RIV06-GA0-21110___" . . "25" . "Topoligick\u00E1 entropie m-n\u00E1sobn\u00FDch zobrazen\u00ED"@cs . . "Topological Entropy of m-fold Maps"@en . "2" . "GB - Spojen\u00E9 kr\u00E1lovstv\u00ED Velk\u00E9 Brit\u00E1nie a Severn\u00EDho Irska" . "P(GA201/03/1153)" . . . "[2C3EF4E4001B]" . "Ergodic Theory and Dynamical Systems" .