Non-uniform stationary measure properties of chaotic area-preserving dynamical systems

Physica A: Statistical Mechanics and its Applications

Volumn 254, Issue 3-4, 1998, Pages 451-465

  Giona, Massimiliano ^a,c   Cerbelli, Stefano ^b   Muzzio, Fernando J ^b   Adrover, Alessandra ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b The State University of New Jersey   (United States)

^c UNIVERSITY OF CAGLIARI   (Italy)

Author keywords

Chaotic Hamiltonian systems; Measure theoretical properties; Two dimensional area preserving maps

Indexed keywords

CHAOS THEORY; CHARACTERIZATION; DENSITY (SPECIFIC GRAVITY); FLUID DYNAMICS; MIXING; TOPOLOGY;

CHAOTIC HAMILTONIAN SYSTEM; LINEAR TORAL AUTOMORPHISM; MEASURE THEORETICAL PROPERTIES; TWO DIMENSIONAL AREA PRESERVING MAPS;

STATISTICAL MECHANICS;

EID: 0032095221     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(97)00666-3     Document Type: Article

References (32)

1. J.D. Farmer, E. Ott, J.A. Yorke, Physica D 7 (1983) 153.
2. H.G.E. Hentschel, I. Procaccia, Physica D 8 (1983) 435.
3. P. Grassberger, I. Procaccia, Physica D 13 (1984) 34.
4. T.C. Halsey, M.J. Jensen, L.P. Kadanoff, I. Procaccia, B.I. Shraiman, Phys. Rev. A 33 (1986) 1141.
5. H. Aref, J. Fluid Mech. 143 (1984) 1.
6. J.M. Ottino, The Kinematics of Mixing: Stretching, Chaos and Transport, Cambridge Univ. Press, Cambridge, 1989.
7. H. Aref, Phil. Trans. R. Soc. Lond. A 333 (1990) 273.
8. P. Grassberger, R. Badii, A. Politi, J. Stat. Phys. 51 (1988) 135.
9. E. Ott, T.M. Antonsen, Phys. Rev. A 39 (1989) 3660.
10. T. Horita, H. Hata, R. Ishizaki, H. Mori, Prog. Theor. Phys. 83 (1990) 1065.
11. F. Városi, T.M. Antonsen, E. Ott, Phys. Fluids A 3 (1991) 1017.
12. V.I. Arnold, A. Avez, Ergodic Problems of Classical Mechanics, Addison-Wesley, New York, 1989.
13. I.P. Cornfeld, S.V. Fomin, Ya.G. Sinai, Ergodic Theory, Springer, Berlin, 1982.
14. V. Rom-Kedar, A. Leonard, S. Wiggins, J. Fluid Mech. 214 (1990) 347.
15. D. Beigie, A. Leonard, S. Wiggins, Phys. Fluids A 3 (1991) 1039.
16. S. Wiggins, Chaotic Transport in Dynamical Systems, Springer, Berlin, 1992.
17. M.M. Alvarez, F.J. Muzzio, S. Cerbelli, A. Adrover, M. Giona, Phys. Rev. Lett., submitted.
18. M. Giona, A. Adrover, F.J. Muzzio, S. Cerbelli, M.M. Alvarez, J. Fluid Mech., submitted.
19. M. Giona, A. Adrover, S. Cerbelli, M.M. Alvarez, F.J. Muzzio, J. Fluid Mech., submitted.
20. D.V. Anosov, Sov. Math. Dokl. 4 (1963) 1153.
21. D.V. Anosov, V.V. Solodov, in: D.V. Anosov (Ed.), Dynamical Systems IX, Encyclopaedia of Math. Sci., Vol. 66, Springer, Berlin, 1995, pp. 10-92.
22. R. Mane, Trans. Am. Math. Soc. 229 (1977) 351.
23. V.I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer, Berlin, 1983.
24. V.K. Melnikov, Trans. Moscow Math. Soc. 12 (1963) 1.
25. S. Wiggins, Global Bifurcations and Chaos - Analytical Methods, Springer, Berlin, 1988.
26. D. Beigie, A. Leonard, S. Wiggins, Chaos Solitons Fractals 4 (1994) 749.
27. D.M. Hobbs, M.M. Alvarez, F.J. Muzzio, Fractals, in press.
28. S. Cerbelli, M. Giona, F.J. Muzzio, A. Adrover, M.M. Alvarez, unpublished.
29. M. Liu, F.J. Muzzio, R.L. Peskin, Chaos Solitons Fractals 4 (1994) 869.
30. A. Lasota, M.M. Mackey, Chaos, Fractals, and Noise, Springer, Berlin, 1994.
31. P. Billingsley, Probability and Measure, Wiley, New York, 1979, p. 367.
32. J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer, Berlin, 1997.