Skip to main content
SpringerLink
Log in

Systoles on Compact Riemann Surfaces with Symbolic Dynamics

  • Conference paper
  • First Online:
Nonlinear Maps and their Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 112))

  • 625 Accesses

Abstract

In this chapter, systolic inequalities are established, precise values are computed, and their behavior is also examined with the variation of the Fenchel–Nielsen coordinates on a compact Riemann surface of genus 2.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bavard, C.: La systole des surfaces hyperelliptiques. Pre publ. no 71 ENS Lyon (1992)

    Google Scholar 

  2. Bavard, C.: Systole et invariant d’Hermite. J. Reine Angew. Math. 482 93–120 (1997)

    Google Scholar 

  3. Beardon, A.: The Geometry of Discrete Groups. Springer, Berlin (1983)

    Book  MATH  Google Scholar 

  4. Berger, M.:A l’ombre de Loewner Ann. Sci. É cole Norm. Sup. \(\textbf5\), 241–260 (1972)

    Google Scholar 

  5. Buser, P., Sarnak, P.: Markov maps associated with Fuchsian groups Invent. Math. 117, 27–56 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  6. Grácio, C., Sousa Ramos, J.: Symbolic dynamics and hyperbolic groups.Grazer Math. Ber. 339, 195–206 (1999)

    MATH  Google Scholar 

  7. Grácio, C., Sousa Ramos, J.: Boundary maps and Fenchel–Nielsen coordinates. Int. J. Bifurc. Chaos Appl. Sci. Eng. 13(7), 1949–1958 (2003)

    Article  MATH  Google Scholar 

  8. Grácio, C., Sousa Ramos, J.: Rigidity and flexibility for surface groups. Grazer Math. Ber. 346, 1189–1195 (2006)

    Google Scholar 

  9. Grácio, C., Sousa Ramos, J.: Geodesic length spectrum on compact Riemann surfaces. J. Geom. Phys. 60, 1643–1655 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  10. Gromov, M., Systoles and intersystolicinequalities. In: Actes de la Table Ronde de Géométrie Diffé rentielle (Luminy 1992), 291–362. Séminaires et Congrès, 1. Soc. Math. France, Institut Henri Poincaré, Paris (1996)

    Google Scholar 

  11. Katz, M., Sabourau, S.: Entropy of systolically extremal surfaces and asymptotic bounds. Ergon. Theory Dyn. Syst. 25, 1209–1220 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  12. Katz, M., Sabourau, S.: Hyperelliptic surfaces are Loewner. Proc. Am. Math. Soc. 134, 1189–1195 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  13. Ymayoshi, Y., Taniguchi, M.: An introduction to teichmuller space. Springer-Verlag (1992)

    Google Scholar 

  14. Maskit, B.: New parameters for Fuchsian groups of genus 2. Proc. Am. Math. Soc. 127(12), 643–3652 (1999)

    Article  MathSciNet  Google Scholar 

  15. McKean, H.: Selberg’s trace formula as applied to a compact Riemann surface. Commun. Pure Appl. Math. XXV, 225–246 (1972)

    Article  MathSciNet  Google Scholar 

  16. Pollicott, M., Rocha, A.: A remarkable formula for the determinant of the laplacian. Invent. Math. 130, 399–414 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  17. Schmutz, P.: Riemann surfaces with shortest geodesic of maximal length. Geom. Funct. Anal. 3, 564–631 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  18. Schmutz, P.: Geometric characterization of hyperelliptic Riemann surfaces. Ann. Acad. Scien. Fenn. Math. 25, 85–90 (2000)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CIMA-UE-DMAT, School of Science and Technology, University of Évora, Rua Romao Ramalho 59, Évora, Portugal

    Clara Grácio

Authors
  1. Clara Grácio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Clara Grácio .

Editor information

Editors and Affiliations

  1. Facultad de Ciencias, Universidad de Zaragoza, Zaragoza, Spain

    Ricardo López-Ruiz

  2. Université de Toulouse, LAAS-CNRS, INSA, Toulouse, France

    Danièle Fournier-Prunaret

  3. Department of E.E. Eng., Tokushima University, Tokushima, Japan

    Yoshifumi Nishio

  4. Department of Mathematics, University of Évora, CIMA-UE, Évora, Portugal

    Clara Grácio

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Grácio, C. (2015). Systoles on Compact Riemann Surfaces with Symbolic Dynamics. In: López-Ruiz, R., Fournier-Prunaret, D., Nishio, Y., Grácio, C. (eds) Nonlinear Maps and their Applications. Springer Proceedings in Mathematics & Statistics, vol 112. Springer, Cham. https://doi.org/10.1007/978-3-319-12328-8_17

Download citation

Publish with us

Policies and ethics

Search

Navigation