In what sense is the kolmogorov-sinai entropy a measure for chaotic behaviour? - Bridging the gap between dynamical systems theory and communication theory

British Journal for the Philosophy of Science

Volumn 55, Issue 3, 2004, Pages 411-434

  Frigg, Roman ^a  

^a LONDON SCHOOL OF ECONOMICS   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 24944455125     PISSN: 00070882     EISSN: None     Source Type: Journal    
DOI: 10.1093/bjps/55.3.411     Document Type: Article

References (26)

1. Alekseev, V. M. & Yakobson, M. V. [1981]: 'Symbolic Dynamics and Hyperbolic Dynamical Systems', Physics Reports, 75, pp. 287-325.
2. Arnold, V. I. & Avez, A. [1968]: Ergodic Problems of Classical Mechanics, New York, NY & Amsterdam: W. A. Benjamin.
3. Batterman, R. [1993]: 'Defining Chaos', Philosophy of Science, 60, pp. 43-66.
4. Batterman, R. & White, H. [1996]; 'Chaos and Algorithmic Complexity', Foundations of Physics, 26, pp. 307-336.
5. Belot, G. & Earman, J. [1997]: 'Chaos out of Order: Quantum Mechanics, the Correspondence Principle and Chaos', Studies in the History and Philosophy of Modern Physics, 28, pp. 147-82.
6. Billingsley, P. [1965]: Ergodic Theory and Information, New York, NY: Wiley.
7. Brudno, A. A. [1978]: The Complexity of the Trajectory of a Dynamical System', Russian Mathematical Surveys, 33, pp. 197-8.
8. Carroll, L. [1998]: Alice's Adventures in Wonderland and Through the Looking-Glass, London: Penguin.
9. Cornfeld, I. P., Fomin, S. V. & Sinai, Y. G. [1982]: Ergodic Theory, Berlin & New York, NY: Springer.
10. Cornfeld, I. P. & Sinai, Y. G. [1980]: 'Entropy Theory of Dynamical Systems', in Y. G. Sinai (ed.), 1980, Dynamical Systems II. Ergodic Theory with Applications to Dynamical Systems and Statistical Mechanics, Berlin & New York, NY: Springer, pp. 36-58.
11. Cover, T. M. & Thomas, J. M. [1991]: Elements of Information Theory, New York, NY & Chichester: Wiley.
12. Earman, J. [1986]: A Primer on Determinism, Dordrecht: Reidel.
13. Eckmann, J.-P. & Ruelle, D. [1985]: 'Ergodic Theory of Chaos and Strange Attractors', Review of Modern Physics, 57, Part I, pp. 617-656.
14. Keller, G. [1998]: Equilibrium States in Ergodic Theory, Cambridge: Cambridge University Press.
15. nd edn, Berlin & New York, NY: Springer.
16. Mañé, R. [1983]: Ergodic Theory and Differentiable Dynamics, Berlin & New York: Springer.
17. Nadkarni, M. G. [1998]: Basic Ergodic Theory, Basel: Birkhäuser.
18. Ott, E. [1993]: Chaos in Dynamical Systems, Cambridge: Cambridge University Press.
19. Parry, W. [1981]: Topics in Ergodic Theory, Cambridge: Cambridge University Press.
20. Petersen, Karl [1983]: Ergodic Theory. London and New York, NY: Cambridge UP.
21. Reichl, L. E. [1992]: The Transition to Chaos in Conservative Classical Systems: Quantum Manifestations, Berlin & New York, NY: Springer.
22. Rudolph, D. J. [1990]: Fundamentals of Measurable Dynamics: Ergodic Theory on Lebesgue Spaces, Oxford: Clarendon Press.
23. nd edn, Weinheim: Physik Verlag.
24. Shannon, C. E. & Weaver, W. [1949]: The Mathematical Theory of Communication, Urbana, Chicago, IL & London: University of Illinois Press.
25. Smith, P. [1998]: Explaining Chaos, Cambridge: Cambridge University Press.
26. Tabor, M. [1989]: Chaos and Integrability in Nonlinear Dynamics, New York, NY: John Wiley & Sons.