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September 12, 2025Ufimskii Matematicheskii ZhurnalOpen Access

On homoclinic points and topological entropy of continuous maps on one - dimensional ramified continua

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Authors

EME. N. Makhrova

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Overview

This analysis examines homoclinic points and their relation to topological entropy in continuous maps, implicating unstable manifolds.

Key Points

  • Homoclinic points' properties affect the dynamic structure of continuous maps on dendroids.
  • The existence of a homoclinic point can imply positive topological entropy for certain continuous functions.
  • Different behaviors of homoclinic points and unstable manifolds are evident between dendroids, dendrites, and finite trees.
  • The study provides a deeper understanding of periodic points and their homoclinic structures.

Cite This Study

E. N. Makhrova (2025) studied this question.

synapsesocial.com/papers/68d44b3031b076d99fa5473fhttps://doi.org/10.13108/2025-17-3-79
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