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Weighted kneading theory of one-dimensional maps with a hole

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  • J. Leonel Rocha
  • J. Sousa Ramos

Abstract

The purpose of this paper is to present a weighted kneading theory for one-dimensional maps with a hole. We consider extensions of the kneading theory of Milnor and Thurston to expanding discontinuous maps with a hole and introduce weights in the formal power series. This method allows us to derive techniques to compute explicitly the topological entropy, the Hausdorff dimension, and the escape rate.

Suggested Citation

  • J. Leonel Rocha & J. Sousa Ramos, 2004. "Weighted kneading theory of one-dimensional maps with a hole," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-20, January.
    • Handle: RePEc:hin:jijmms:787398
    DOI: 10.1155/S016117120430428X
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    Cited by:

    1. Caneco, Acilina & Grácio, Clara & Leonel Rocha, J., 2009. "Kneading theory analysis of the Duffing equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1529-1538.
    2. J. Leonel Rocha & Sónia Carvalho & Beatriz Coimbra & Inês Henriques & Juliana Pereira, 2023. "Influence Maximization Dynamics and Topological Order on Erdös-Rényi Networks," Mathematics, MDPI, vol. 11(15), pages 1-18, July.
    3. Leonel Rocha, J. & Carvalho, S., 2021. "Information theory, synchronization and topological order in complete dynamical networks of discontinuous maps," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 340-352.

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