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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Monotone Maps on Dendrites

Discontinuity, Nonlinearity, and Complexity 9(4) (2020) 541--552 | DOI:10.5890/DNC.2020.12.007

E. N. Makhrova

Lobachevsky State University of Nizhni Novgorod, Gagarin ave., 23, Nizhni Novgorod, 603095, Russia

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Let $X$ be a dendrite, $f:X\to X$ be a monotone map. In the article the relationship between a structure of a dendrite $X$ and dynamical properties of $f$ is studied. Namely the relation between a structure of $X$ and a structure of the sets of periodic points of $f$, non-wandering points of $f$, $\omega$-limit sets of trajectories is established. The structure of dendrites on which there exist monotone pointwise chain recurrent maps is characterized. The structure of dendrites on which there exist monotone maps with homoclinic points is described.


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