Topological conjugation of one dimensional maps
Makar Plakhotnyk
TL;DR
This paper investigates the topological conjugation of one-dimensional unimodal maps, focusing on the smoothness, differentiability, and extremal properties of conjugacies between symmetrical and non-symmetrical tent maps.
Contribution
It provides new insights into the smoothness and extremal properties of conjugacies for unimodal maps, specifically tent maps, expanding understanding of their topological and geometric characteristics.
Findings
Analyzed the smoothness and differentiability of conjugacies.
Proved extremal properties of the graph length of conjugacies.
Compared symmetrical and non-symmetrical tent maps.
Abstract
Topological conjugateness of one dimensional unimodal dynamical systems, which are generated by interval [0, 1] into itself maps are studied. We study the smoothness and differentiability of the conjugacy of symmetrical and non-symmetrical tent maps. Also weprove the extremal property of the length of the graph of the conjugacy of symmetrical and non-symmetrical tent maps.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Chaos control and synchronization · Quantum chaos and dynamical systems