Contracting-on-average Baker maps

• Autorzy: Rams M.
• Języki publikacji: EN

Abstrakty

EN

We estimate from above and below the Hausdorff dimension of SRB measure for contracting-on-average baker maps.

Słowa kluczowe

EN

baker map; Hausdorff dimension; SRB measure; transversality condition

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2006
• Tom: Vol. 54, no 3-4
• Strony: 219--229
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Rams M.

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland,

Bibliografia

• [B] H. G. Bothe, The Hausdorff dimension of certain solenoids, Ergodic Theory Dynam. Systems 15 (1995), 449-474.
• [Bo] R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Springer, Heidelberg, 1975.
• [F] K. Falconer, Techniques in Fractal Geometry, Wiley, Chichester, 1997.
• [PS] M. Pollicott and K. Simon, The Hausdorff dimension of X-expansions with deleted digits, Trans. Amer. Math. Soc. 347 (1995), 967-983.
• [Rl] M. Rams, Absolute continuity of the SBR measure for non-linear fat baker maps, Nonlinearity 16 (2003), 1649-1655.
• [R2] —, Dimension estimates for invariant measures of contracting-on-average iterated function systems, preprint.
• [RS] M. Rams and K. Simon, Hausdorff and packing measure for solenoids, Ergodic Theory Dynam. Systems 23 (2003), 273-292.
• [SI] K. Simon, Hausdorff dimension for non-invertible maps, ibid. 13 (1993), 199-212.
• [S2] —, The Hausdorff dimension of the general Smale-Williams solenoid, Proc. Amer. Math. Soc. 125 (1997), 1221-1228.
• [SS] K. Simon and B. Solomyak, Hausdorff dimension for horseshoes in R3, Ergodic Theory Dynam. Systems 19 (1999), 1343-1363.
• [T] M. Tsujii, Fat solenoidal attractors, Nonlinearity 14 (2001), 1011-1027.