Skip to main content
SpringerLink
Log in

Symbolic Encoding in Dynamical Systems

  • Chapter
From Statistical Physics to Statistical Inference and Back

Part of the book series: NATO ASI Series ((ASIC,volume 428))

  • 348 Accesses

Abstract

The methods to encode the dynamical behaviour of strange attractors are reviewed, with particular emphasis given to the construction of generating partitions from homoclinic tangencies. The topological properties of the associated symbol sequences are then investigated through a systematic search of forbidden words. Generating partitions — Graphs — Formal languages

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 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Artin, E. and Mazur, B.: 1965, Ann. Math. Series 2 81, 82

    Article  MathSciNet  MATH  Google Scholar 

  2. Artuso, R., Aurell, E. and Cvitanović, P.: 1990 Nonlinearity 3, 325

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. Badii, R. and Politi, A.: unpublished

    Google Scholar 

  4. Biham, O. and Wenzel, W.: 1989, Phys. Rev. Lett. 63,8:9

    Article  MathSciNet  Google Scholar 

  5. Collet, P. and Eckmann, J.-P.: 1980, Iterated Maps on the Interval as Dynamical Systems, Birkhäuser: Boston

    MATH  Google Scholar 

  6. Cvetkovic, D. Doob, M. and Sachs, H.: 1980, Spectra of graphs, Academic Press: New York

    Google Scholar 

  7. Cvitanovic, P.: 1988 Phys. Rev. Lett. 61, 2729

    Article  MathSciNet  ADS  Google Scholar 

  8. Cvitanovic, P. Gunaratne, G.H. and Procaccia, I.: 1988, Phys. Rev. A 38, 1503

    Article  MathSciNet  ADS  Google Scholar 

  9. D’Alessandro, G. and Politi, A.: 1990, Phys. Rev. Lett. 64, 1609

    Article  MathSciNet  ADS  Google Scholar 

  10. D’Alessandro, F. Isola, S. and Politi, A.: 1991, Prog. Theor. Phys. 86, 1149

    Article  MathSciNet  ADS  Google Scholar 

  11. D’Alessandro, G. Grassberger, P. Isola, S. and Politi, A.: 1990 J. Phys. A: Math. Gen. 23, 5285

    Article  MathSciNet  ADS  Google Scholar 

  12. Giovannini, F. and Politi, A.: 1991, J. Phys. A: Math. Gen. 24, 1837

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. Giovannini, F. and Politi, A.: 1992, Phys. Lett. A161, 332

    MathSciNet  ADS  Google Scholar 

  14. Grassberger, P.: 1988, Z. für Naturforschung 43A, 671

    MathSciNet  Google Scholar 

  15. Grassberger, P. and Kantz, H.: 1985, Phys. Lett. 113A, 235

    MathSciNet  ADS  Google Scholar 

  16. Grassberger, P. Kantz, H. and Moenig, U.: 1989, I. Phys. A: Math. Gen. 43, 5217

    Article  MathSciNet  ADS  Google Scholar 

  17. Hansen, K.: 1992, Phys. Lett. A165, 100

    ADS  Google Scholar 

  18. Hopcroft, H.E. and Ullman, J.D.: 1979, Introduction to automata theory, languages, and computation, Addison-Wesley: Reading, MA

    MATH  Google Scholar 

  19. Isola, S. and Politi, A.: 1990, J. Stat. Phys. 61, 263

    Article  MathSciNet  ADS  Google Scholar 

  20. Milnor, J. and Thurston, W.: 1988, Lect. Notes in Math. 1342 ( Dold, A. and Eckmann, B. eds.), Springer Verlag: Berlin, 465

    Google Scholar 

  21. Ruelle, D.: 1978, Thermodynamic Formalism, Addison-Wesley: Reading, MA

    MATH  Google Scholar 

  22. Sinai, Ya.G.: 1972, Russ. Math. Surv. 27, 21

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. Smale, S.: 1967 Bull. AMS 73, 747

    Article  MathSciNet  MATH  Google Scholar 

  24. Tel, T.: 1983 Phys. Lett. 97A, 219

    MathSciNet  ADS  Google Scholar 

  25. Wenzel, W. Biham, O. and Jayaprakash, C: 1991, Phys. Rev. A 43, 6550

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Istituto Nazionale di Ottica, I-50125, Firenze, Italy

    Antonio Politi

  2. INFN Sezione di Firenze, Italy

    Antonio Politi

Authors
  1. Antonio Politi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Theoretical Physics, University of Wuppertal, Wuppertal, Germany

    Peter Grassberger

  2. Laboratory of Statistical Physics, École Normale Supérieure, Paris, France

    Jean-Pierre Nadal

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Politi, A. (1994). Symbolic Encoding in Dynamical Systems. In: Grassberger, P., Nadal, JP. (eds) From Statistical Physics to Statistical Inference and Back. NATO ASI Series, vol 428. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1068-6_19

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-1068-6_19

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4465-3

  • Online ISBN: 978-94-011-1068-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation