Skip to main content
  • 3009 Accesses

Abstract

Recently, the Science and Technology Foundation of Japan announced that James A. Yorke had been named a winner of the 2003 Japan Prize for his work in the field of chaos theory. This foundation has awarded Japan Prizes since 1985 under the auspices of the Japanese prime minister. It is a Japanese ver­sion of the Nobel Prize. One of the most esteemed of science and technology prizes, Japan Prizes are given to scientists whose “original and outstanding achievements in science and technology are recognized as having advanced the frontiers of knowledge and served the cause of peace and prosperity for mankind.” The Science and Technology Foundation of Japan announced that Yorke and Benoit Mandelbrot, of Yale University, will share $415,000 (50 mil­lion yen) for the “creation of universal concepts in complex systems: chaos and fractals”. The other 2003 Japan Prize was awarded for discovering the principle behind magnetic resonance imaging (MRI). Past Japan prizes have been awarded for achievements such as the discovery of the HIV virus, the invention of the World Wide Web, the development of artificial intelligence, and the eradication of smallpox. “For a scientist to be awarded the Japan Prize is a distinction as great as any in the world,” said University of Mary­land President C.D. Mote, Jr. “Jim Yorke has now been officially recognized for his original achievements in nonlinear dynamics that have monumentally advanced the frontiers of science and technology and served the cause of peace and prosperity for mankind. I am so pleased for him and for the inspiration his recognition will provide for others who by pursuing their passions can hope to have an impact as great as Jim’s.” The presentation ceremony for the 2003 Japan Prize laureates is scheduled to be held in Tokyo in April 2003.

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

Access this chapter

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 PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.F. Alves, C. Bonatti and M. Viana, SRB measures for partially hyperbolic systems whose central direction is mostly expanding, Invent. Math. 140 (2000), 351–398

    MathSciNet  MATH  Google Scholar 

  2. M. Benedicks and L. Carleson, The dynamics of the Hénon map, Annals of Math. 133 (1991), 73–169

    Article  MathSciNet  MATH  Google Scholar 

  3. M. Benedicks and L.-S. Young, Sinai-Bowen-Ruelle measures for certain Hénon maps, Invent. Math. 112 (1993), 541–576

    MathSciNet  MATH  Google Scholar 

  4. R. Bowen and D. Ruelle, The ergodic theory of Axiom A flows, Invent. Math. 29 (1975), 181–202

    MathSciNet  MATH  Google Scholar 

  5. P. Collet and Y. Levy, Ergodic properties of the Lozi mappings, Commun. Math. Phys. 93 (1984), 461–481

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Dellnitz and O. Junge, On the approximation of complicated dynamical behavior, SIAM J. Numer. Anal. 36 (1999), 491–515

    Article  MathSciNet  Google Scholar 

  7. J.-P. Eckmann, Roads to turbulence in dissipative dynamical systems, Rev. Modern Phys. 53 (1981), 643–654

    Article  MathSciNet  MATH  Google Scholar 

  8. J.-P. Eckmann and D. Ruelle, Ergodic theory of chaos and strange at-tractors, Rev. Modern Phys. 57 (1985), 617–656

    Article  MathSciNet  Google Scholar 

  9. J.D. Farmer, E. Ott and J.A. Yorke, The dimension of chaotic attractors, Physica D 7 (1983), 153–180

    Article  MathSciNet  Google Scholar 

  10. P. Gora and A. Boyarsky, Absolutely continuous invariant measures for piecewise expanding C2 transformation in R N,Israel J. Math. 67(1989), 272286

    Google Scholar 

  11. P. Grassberger and I. Procaccia, Measuring the strangeness of strange attractors, Physica D 9 (1983), 189–208

    Article  MathSciNet  MATH  Google Scholar 

  12. C. Grebogi, E. Ott and J.A. Yorke, Crisis, sudden changes in chaotic attractors, and transient chaos, Physica D 7 (1983), 181–200

    Article  MathSciNet  Google Scholar 

  13. C. Grebogi, E. Ott, and J.A. Yorke, Unstable periodic orbits and the dimensions of multifractal chaotic attractors, Phys. Rev. A 37(1988), 17111724

    Google Scholar 

  14. M. Hénon, A two-dimensional mapping with a strange attractor, Commun. Math. Phys. 50 (1976), 69–77

    Google Scholar 

  15. F. Hofbauer and G. Keller, Ergodic properties of invariant measures for piecewise monotonic transformations, Math. Z. 180 (1982), 119–140

    Article  MathSciNet  MATH  Google Scholar 

  16. B.R. Hunt, J.A. Kennedy, T.-Y. Li and H.E. Nusse, SLYRB measures: natural invariant measures for chaotic systems, Physica D 170 (2002), 50–71

    Article  MathSciNet  MATH  Google Scholar 

  17. M. Jakobson, Chaotic behavior of multidimensional difference equations, in Functional Differential Equations and Approximation of Fixed Points, H.O. Peitgen and H.O. Walther, eds., Springer Lecture Notes in Mathematics #730 (1979), 204–227

    Google Scholar 

  18. K. Krzyzewski and W. Szlenk, On invariant measures for expanding differentiable mappings, Studia Math. 33 (1969), 83–92

    MathSciNet  MATH  Google Scholar 

  19. A. Lasota and J.A. Yorke, On the existence of invariant measures for piecewise monotonic transformations, Trans. Amer. Math. Soc. 186 (1973), 481–488

    Article  MathSciNet  Google Scholar 

  20. F. Ledrappier, Proprietes ergodiques des mesures de Sinai, I.H.E.S. Publ. Math. 59 (1984), 163–188

    MathSciNet  MATH  Google Scholar 

  21. T.-Y. Li and J.A. Yorke, Period three implies chaos, Amer. Math. Monthly 82 (1975), 985–992

    Article  MathSciNet  MATH  Google Scholar 

  22. T.-Y. Li and J.A. Yorke, Ergodic transformations from an interval into itself, Trans. Amer. Math. Soc. 235 (1978), 183–192

    Article  MathSciNet  MATH  Google Scholar 

  23. E.N. Lorenz, Deterministic nonperiodic flow, J. Atm. Sc. 20(1963), 130–24 Introduction

    Google Scholar 

  24. du type attracteur de Hénon, J. Physique (Paris) 39 ( Coll. C5 ) (1978), 9–10

    Google Scholar 

  25. R.M. May, Simple mathematical models with very complicated dynamics, Nature 261 (1976), 459–467

    Article  Google Scholar 

  26. J. Milnor, On the concept of attractor, Commun. Math. Phys. 99 (1985), 177–195; Comments “On the concept of attractor”: corrections and remarks, Commun. Math. Phys. 102 (1985), 517–519

    MathSciNet  MATH  Google Scholar 

  27. M. Misiurewicz, Strange attractors for the Lozi mappings, in Nonlinear Dynamics, R.H.G. Heileman, ed., Ann. New York Acad. Sci. #357 (1980), 348–358

    Google Scholar 

  28. E. Ott, Strange attractors and chaotic motions of dynamical systems, Rev. Modern Phys. 53 (1981), 655–671

    Article  MathSciNet  MATH  Google Scholar 

  29. E. Ott, Chaos in Dynamical Systems, Cambridge University Press, 1993 [P] Ya.B. Pesin, Dimension Theory in Dynamical Systems, Contemporary Views and Applications, University of Chicago Press, 1997

    Google Scholar 

  30. O. Rössler, Horseshoe map chaos in the Lorenz equation, Phys. Lett. A 60 (1977), 392–394

    Article  Google Scholar 

  31. D. Ruelle and F. Takens, On the nature of turbulence, Commun. Math. Phys. 20 (1971), 167–192

    Article  MathSciNet  MATH  Google Scholar 

  32. M.R. Rychlik, Another proof of Jakobson’s theorem and related results, Ergodic Theory Dynamical Systems 8 (1988), 93–109

    Article  MathSciNet  MATH  Google Scholar 

  33. M. Rychlik, Mesures invariantes et principe variationel pour les applications de Lozi, C.R. Acad. Sc. Paris, t. 296 (1983), 19–22

    MathSciNet  Google Scholar 

  34. M. Rychlik, Invariant Measures and Variational Principle for Lozi Applications, Ph.D. dissertation, University of California at Berkeley (1983), [Sa] A.N. Sarkovskii, Coexistence of cycles of a continuous map of the line into itself, Ukr. Mat. Z. 16 (1964), 61–71

    Google Scholar 

  35. Ya.G. Sinai, Gibbs measures in ergodic theory, Russian Mathematical Surveys 27 (1972), 21–69

    Google Scholar 

  36. P. Stefan, 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 

  37. M. Tsujii, On continuity of Bowen-Ruelle-Sinai measures in families of one dimensional maps, Comm. Math. Phys. 177 (1996), 1–11

    Article  MathSciNet  MATH  Google Scholar 

  38. M. Tsujii, Absolutely continuous invariant measures for piecewise real-analytic expanding maps on the plane, Comm. Math. Phys. 208 (2000), 605622

    Google Scholar 

  39. J.A. Yorke and E.D. Yorke, Metastable chaos: the transition to sustained chaotic behavior in the Lorenz model, J. Stat. Phys. 21 (1979), 263–277

    Article  MathSciNet  Google Scholar 

  40. L.-S. Young, Bowen-Ruelle measures for certain piecewise hyperbolic maps, Trans. Amer. Math. Soc. 287 (1985), 41–48

    Article  MathSciNet  MATH  Google Scholar 

  41. L.-S. Young, Statistical properties of dynamical systems with some hyperbolicity, Ann. of Math. (2) 147 (1998), 585–650

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer Science+Business Media New York

About this chapter

Cite this chapter

Hunt, B.R., Li, TY., Kennedy, J.A., Nusse, H.E. (2004). Introduction. In: Hunt, B.R., Li, TY., Kennedy, J.A., Nusse, H.E. (eds) The Theory of Chaotic Attractors. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21830-4_1

Download citation

  • DOI: https://doi.org/10.1007/978-0-387-21830-4_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-2330-1

  • Online ISBN: 978-0-387-21830-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics