# Classification of one dimensional dynamical systems by countable structures

@article{Bruin2020ClassificationOO, title={Classification of one dimensional dynamical systems by countable structures}, author={H. Bruin and B. Vejnar}, journal={arXiv: Dynamical Systems}, year={2020} }

We study the complexity of the classification problem of conjugacy on dynamical systems on some compact metrizable spaces. Especially we prove that the conjugacy equivalence relation of interval dynamical systems is Borel bireducible to isomorphism equivalence relation of countable graphs. This solves a special case of the Hjorth's conjecture which states that every orbit equivalence relation induced by a continuous action of the group of all homeomorphisms of the closed unit interval is… Expand

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