-
Previous Article
From one-sided dichotomies to two-sided dichotomies
- DCDS Home
- This Issue
- Next Article
On the asymptotics of the scenery flow
1. | Centre for Mathematical Sciences, Lund University, Box 118, 22 100 Lund, Sweden, Sweden, Sweden |
2. | Centre for Mathematical Sciences, Lund University, P.O. Box 118, SE-221 00 Lund |
References:
[1] |
C. Bandt, The Tangent Distribution for Self-Similar Measures, Lecture at the 5th Conference on Real Analysis and Measure Theory, 1992. |
[2] |
K. Falconer, Techniques in Fractal Geometry, John Wiley & sons, Chichester, 1997. |
[3] |
M. Gavish, Measures with uniform scaling scenery, Ergod. Th. & Dynam. Sys., 31 (2011), 33-48.
doi: 10.1017/S0143385709000996. |
[4] |
S. Graf, On Bandt's tangential distribution for self-similar measures, Monatsh. Math., 120 (1995), 223-246.
doi: 10.1007/BF01294859. |
[5] |
M. Hochman, Geometric rigidity of $\times m$ invariant measures, J. Eur. Math. Soc., 14 (2012), 1539-1563.
doi: 10.4171/JEMS/340. |
[6] |
M. Hochman, Dynamics on fractals and fractal distributions, preprint, arXiv:1008.3731, 2013. |
[7] |
M. Hochman, Erratum to "Geometric rigidity of $\times m$ invariant measures'', J. Eur. Math. Soc., 15 (2013), 2463-2464.
doi: 10.4171/JEMS/425. |
[8] |
D. W. Stroock, Probability Theory, an Analytic View, Cambridge University Press, Cambridge, 1993. |
show all references
References:
[1] |
C. Bandt, The Tangent Distribution for Self-Similar Measures, Lecture at the 5th Conference on Real Analysis and Measure Theory, 1992. |
[2] |
K. Falconer, Techniques in Fractal Geometry, John Wiley & sons, Chichester, 1997. |
[3] |
M. Gavish, Measures with uniform scaling scenery, Ergod. Th. & Dynam. Sys., 31 (2011), 33-48.
doi: 10.1017/S0143385709000996. |
[4] |
S. Graf, On Bandt's tangential distribution for self-similar measures, Monatsh. Math., 120 (1995), 223-246.
doi: 10.1007/BF01294859. |
[5] |
M. Hochman, Geometric rigidity of $\times m$ invariant measures, J. Eur. Math. Soc., 14 (2012), 1539-1563.
doi: 10.4171/JEMS/340. |
[6] |
M. Hochman, Dynamics on fractals and fractal distributions, preprint, arXiv:1008.3731, 2013. |
[7] |
M. Hochman, Erratum to "Geometric rigidity of $\times m$ invariant measures'', J. Eur. Math. Soc., 15 (2013), 2463-2464.
doi: 10.4171/JEMS/425. |
[8] |
D. W. Stroock, Probability Theory, an Analytic View, Cambridge University Press, Cambridge, 1993. |
[1] |
Luis Barreira and Jorg Schmeling. Invariant sets with zero measure and full Hausdorff dimension. Electronic Research Announcements, 1997, 3: 114-118. |
[2] |
Jon Chaika. Hausdorff dimension for ergodic measures of interval exchange transformations. Journal of Modern Dynamics, 2008, 2 (3) : 457-464. doi: 10.3934/jmd.2008.2.457 |
[3] |
Davit Karagulyan. Hausdorff dimension of a class of three-interval exchange maps. Discrete and Continuous Dynamical Systems, 2020, 40 (3) : 1257-1281. doi: 10.3934/dcds.2020077 |
[4] |
Krzysztof Barański. Hausdorff dimension of self-affine limit sets with an invariant direction. Discrete and Continuous Dynamical Systems, 2008, 21 (4) : 1015-1023. doi: 10.3934/dcds.2008.21.1015 |
[5] |
V. V. Chepyzhov, A. A. Ilyin. On the fractal dimension of invariant sets: Applications to Navier-Stokes equations. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 117-135. doi: 10.3934/dcds.2004.10.117 |
[6] |
Yan Wang, Guanggan Chen. Invariant measure of stochastic fractional Burgers equation with degenerate noise on a bounded interval. Communications on Pure and Applied Analysis, 2019, 18 (6) : 3121-3135. doi: 10.3934/cpaa.2019140 |
[7] |
Michael L. Frankel, Victor Roytburd. Fractal dimension of attractors for a Stefan problem. Conference Publications, 2003, 2003 (Special) : 281-287. doi: 10.3934/proc.2003.2003.281 |
[8] |
Michael Hochman. Lectures on dynamics, fractal geometry, and metric number theory. Journal of Modern Dynamics, 2014, 8 (3&4) : 437-497. doi: 10.3934/jmd.2014.8.437 |
[9] |
Michael Barnsley, James Keesling, Mrinal Kanti Roychowdhury. Special issue on fractal geometry, dynamical systems, and their applications. Discrete and Continuous Dynamical Systems - S, 2019, 12 (8) : i-i. doi: 10.3934/dcdss.201908i |
[10] |
Tomasz Szarek, Mariusz Urbański, Anna Zdunik. Continuity of Hausdorff measure for conformal dynamical systems. Discrete and Continuous Dynamical Systems, 2013, 33 (10) : 4647-4692. doi: 10.3934/dcds.2013.33.4647 |
[11] |
Hiroki Sumi, Mariusz Urbański. Bowen parameter and Hausdorff dimension for expanding rational semigroups. Discrete and Continuous Dynamical Systems, 2012, 32 (7) : 2591-2606. doi: 10.3934/dcds.2012.32.2591 |
[12] |
Sara Munday. On Hausdorff dimension and cusp excursions for Fuchsian groups. Discrete and Continuous Dynamical Systems, 2012, 32 (7) : 2503-2520. doi: 10.3934/dcds.2012.32.2503 |
[13] |
Shmuel Friedland, Gunter Ochs. Hausdorff dimension, strong hyperbolicity and complex dynamics. Discrete and Continuous Dynamical Systems, 1998, 4 (3) : 405-430. doi: 10.3934/dcds.1998.4.405 |
[14] |
Krzysztof Barański, Michał Wardal. On the Hausdorff dimension of the Sierpiński Julia sets. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 3293-3313. doi: 10.3934/dcds.2015.35.3293 |
[15] |
Joseph Squillace. Estimating the fractal dimension of sets determined by nonergodic parameters. Discrete and Continuous Dynamical Systems, 2017, 37 (11) : 5843-5859. doi: 10.3934/dcds.2017254 |
[16] |
Yuanhong Chen, Chao Ma, Jun Wu. Moving recurrent properties for the doubling map on the unit interval. Discrete and Continuous Dynamical Systems, 2016, 36 (6) : 2969-2979. doi: 10.3934/dcds.2016.36.2969 |
[17] |
Jian Zhai, Jianping Fang, Lanjun Li. Wave map with potential and hypersurface flow. Conference Publications, 2005, 2005 (Special) : 940-946. doi: 10.3934/proc.2005.2005.940 |
[18] |
Hsuan-Wen Su. Finding invariant tori with Poincare's map. Communications on Pure and Applied Analysis, 2008, 7 (2) : 433-443. doi: 10.3934/cpaa.2008.7.433 |
[19] |
Lulu Fang, Min Wu. Hausdorff dimension of certain sets arising in Engel continued fractions. Discrete and Continuous Dynamical Systems, 2018, 38 (5) : 2375-2393. doi: 10.3934/dcds.2018098 |
[20] |
Thomas Jordan, Mark Pollicott. The Hausdorff dimension of measures for iterated function systems which contract on average. Discrete and Continuous Dynamical Systems, 2008, 22 (1&2) : 235-246. doi: 10.3934/dcds.2008.22.235 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]