Fractal Dimension of Cantori

citation information (sept 2004, from ISI web of knowledge)

1. 
       Garcia-Garcia AM, Verbaarschot JJM
       Critical statistics in quantum chaos and Calogero-Sutherland model at finite
       temperature 
       PHYSICAL REVIEW E 67 (4): Art. No. 046104 Part 2 APR 2003 
    2. 
       FEUDEL U, KURTHS J, PIKOVSKY AS
       STRANGE NONCHAOTIC ATTRACTOR IN A QUASI-PERIODICALLY
       FORCED CIRCLE MAP 
       PHYSICA D 88 (3-4): 176-186 DEC 1 1995 
    3. 
       MOREIRA JG, SALINAS SR
       MODULATED STRUCTURES IN THE ISING-MODEL WITH COMPETING
       INTERACTIONS ON THE CAYLEY TREE 
       PHYSICAL REVIEW B 47 (2): 778-786 JAN 1 1993 
    4. 
       COUTINHO R, LIMA R, MENDES RV, et al.
       LOGARITHMIC MEASURES, SUBDIMENSION AND LYAPUNOV EXPONENTS
       OF CANTORI 
       ANNALES DE L INSTITUT HENRI POINCARE-PHYSIQUE THEORIQUE 56 (4):
       415-427 1992 
    5. 
       MEISS JD
       SYMPLECTIC MAPS, VARIATIONAL-PRINCIPLES, AND TRANSPORT 
       REVIEWS OF MODERN PHYSICS 64 (3): 795-848 JUL 1992 
[a review]

    6. 
       VEERMAN JJP, TANGERMAN FM
       INTERSECTION-PROPERTIES OF INVARIANT-MANIFOLDS IN CERTAIN
       TWIST MAPS 
       COMMUNICATIONS IN MATHEMATICAL PHYSICS 139 (2): 245-265 1991 
    7. 
       WENZEL W, BIHAM O, JAYAPRAKASH C
       PERIODIC-ORBITS IN THE DISSIPATIVE STANDARD MAP 
       PHYSICAL REVIEW A 43 (12): 6550-6557 JUN 15 1991 
    8. 
       VEERMAN JJP, TANGERMAN FM
       ON AUBRY-MATHER SETS 
       PHYSICA D 46 (2): 149-162 NOV 1990 
    9. 
       CHEN Q, DANA I, MEISS JD, et al.
       RESONANCES AND TRANSPORT IN THE SAWTOOTH MAP 
       PHYSICA D 46 (2): 217-240 NOV 1990 
    10. 
       MATIOLI GT
       ON THE TOPOLOGY OF NORMAL CHROMATIDS AND ON THEIR
       TRANSLOCATIONS IN MYELOGENOUS LEUKEMIA 
       MEDICAL HYPOTHESES 32 (1): 11-19 MAY 1990 

11. 
       VEERMAN JJP, TANGERMAN FM
       RENORMALIZATION OF AUBRY-MATHER CANTOR SETS 
       JOURNAL OF STATISTICAL PHYSICS 56 (1-2): 83-98 JUL 1989 
    12. 
       BIHAM O, MUKAMEL D
       GLOBAL UNIVERSALITY IN THE FRENKEL-KONTOROVA MODEL 
       PHYSICAL REVIEW A 39 (10): 5326-5335 MAY 15 1989 
    13. 
       SCHELLNHUBER HJ, URBSCHAT H
       ANALYTICAL STUDY OF CANTORI - GAP STRUCTURE, INITIAL
       CONDITIONS, AND DIMENSIONS 
       PHYSICAL REVIEW A 38 (11): 5888-5901 DEC 1 1988 
    14. 
       JOHANNESSON H, SCHAUB B, SUHL H
       CRITICAL EXPONENTS FOR AN INCOMMENSURATE STRUCTURE WITH
       SEVERAL LENGTH SCALES 
       PHYSICAL REVIEW B 37 (16): 9625-9637 JUN 1 1988 
    15. 
       GREENE JM, JOHANNESSON H, SCHAUB B, et al.
       SCALING ANOMALY AT THE CRITICAL TRANSITION OF AN
       INCOMMENSURATE STRUCTURE 
       PHYSICAL REVIEW A 36 (12): 5858-5861 DEC 15 1987 
    16. 
       MACKAY RS, MEISS JD, PERCIVAL IC
       RESONANCES IN AREA-PRESERVING MAPS 
       PHYSICA D 27 (1-2): 1-20 JUL 1987 
    17. 
       MACKAY RS
       HYPERBOLIC CANTORI HAVE DIMENSION ZERO 
       JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL 20 (9):
       L559-L561 JUN 21 1987 
[Assuming "hyperbolic", the D=0 result for cantori is proved.]

    18. 
       SCHELLNHUBER HJ, URBSCHAT H
       ANALYTICITY BREAKING OF WAVE-FUNCTIONS AND FRACTAL
       PHASE-DIAGRAM FOR SIMPLE INCOMMENSURATE SYSTEMS 
       PHYSICA STATUS SOLIDI B-BASIC RESEARCH 140 (2): 509-519 APR 1987 
    19. 
       BLOCK A, SCHELLNHUBER HJ, URBSCHAT H
       ANALYTIC FRACTAL DIMENSION OF CANTORI 
       PHYSICAL REVIEW LETTERS 58 (10): 1046-1046 MAR 9 1987 
[They say the same result for another map can be obtained analytically.]

other information:

• The idea of this project was due to Sergei Burkov, then at the Laudau Institute at Soviet Union
• Robert Sinclair MacKay's thesis, Renomalisation in Area Preserving Maps (Ph.D Thesis, Department of Astrophysical Sciences, Princeton University, 1982), was the bible on this topic for me. We just found a small thing he didn't do...