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Chaotic mappings on S1 periods one, two, three imply chaos on S1

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Numerical Solution of Nonlinear Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 878))

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References

  1. L. BLOCK: Periodic points of continuous mappings of the circle, Trans. AMS 260 (1980), 555–562

    Article  MathSciNet  Google Scholar 

  2. L. BLOCK, J. GUCKENHEIMER, M. MISIUREWICZ, L-S. YOUNG: Periodic points and topological entropy of one dimensional maps, in ‘Global Theory of Dynamical Systems’ Springer Lecture Notes in Mathematics, vol 819 (1980), 18–34

    Article  MathSciNet  MATH  Google Scholar 

  3. R. BOWEN, J. FRANKS: The periodic points of maps of the disk and the interval, Topology 15 (1976), 337–342

    Article  MathSciNet  MATH  Google Scholar 

  4. C. BOWSZYC: Fixed point theorems for the pairs of spaces, Bull. Acad. Polon. Sci. 16 (1968), 845–850

    MathSciNet  MATH  Google Scholar 

  5. R.F. BROWN: The Lefschetz Fixed Point Theorem, Scott, Foresman and Comp. Glenview, Illinois (1971)

    MATH  Google Scholar 

  6. M. GREENBERG: Lectures on Algebraic Topology, New York, Benjamin, (1967)

    MATH  Google Scholar 

  7. J. GUCKENHEIMER: Bifurcations of maps of the interval, Inventiones Math. 39 (1977), 165–178

    Article  MathSciNet  MATH  Google Scholar 

  8. T-Y. LI, J.A. YORKE: Period three implies chaos, Amer. Math. Monthly 82 (1975), 985–992

    Article  MathSciNet  MATH  Google Scholar 

  9. A. MANNING: Topological entropy and the first homology group, in ‘Dynamical Systems-Warwick 1974’ Springer Lecture Notes in Mathematics, vol 468 (1975), 185–190

    Article  MathSciNet  MATH  Google Scholar 

  10. F.R. MAROTTO: Snap-back repellers imply chaos in Rn, J. Math. Anal. and Appl. 63 (1978), 199–223

    Article  MathSciNet  MATH  Google Scholar 

  11. R.M. MAY: Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos, Science 186 (1974), 645–647

    Article  Google Scholar 

  12. A.N. ŠARKOVSKII: Coexistence of cycles of a continuous map of a line into itself, Ukr. Mat. Z. 16 (1964), 61–71

    Google Scholar 

  13. P. ŠTEFAN: A theorem of Sarkovskii on the existence of periodic orbits of continuous endomorphisms of the real line, Comm. Math. Phys. 54 (1977), 237–248

    Article  MathSciNet  MATH  Google Scholar 

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  1. Forschungsschwerpunkt "Dynamische Systeme" Fachbereich Mathematik, Universität Bremen, D-2800, Bremen 33

    H. -W. Siegberg

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  1. H. -W. Siegberg
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Eugene L. Allgower Klaus Glashoff Heinz-Otto Peitgen

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© 1981 Springer-Verlag

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Siegberg, H.W. (1981). Chaotic mappings on S1 periods one, two, three imply chaos on S1 . In: Allgower, E.L., Glashoff, K., Peitgen, HO. (eds) Numerical Solution of Nonlinear Equations. Lecture Notes in Mathematics, vol 878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090688

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  • DOI: https://doi.org/10.1007/BFb0090688

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10871-9

  • Online ISBN: 978-3-540-38781-7

  • eBook Packages: Springer Book Archive

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