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VIDEO LIBRARY |
International Conference "Functions Theory, Operators Theory and Quantum Information Theory"
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On criteria for the positiveness of the topological entropy of continuous mappings on dendrites E. N. Makhrova |
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Abstract: By continuum we mean a compact connected metric space. A dendrite is a locally connected continuum that does not contain subsets homeomorphic to a circle. Let A dendrite with a finite number of endpoints is called a finite tree. Note that any two points For a continuous mapping (1) the topological entropy (2) for some natural number (3) (4) The paper studies the connections between statements (1) – (4) for continuous mappings on dendrites that are not finite trees. It has been established that the implications between (1) – (4) depend on the structure of the dendrite. |