# American Institute of Mathematical Sciences

July  2015, 35(7): 2797-2815. doi: 10.3934/dcds.2015.35.2797

## 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

Received  June 2014 Revised  December 2014 Published  January 2015

We study the asymptotics of the scenery flow. We give corrected versions with proofs of a certain lemma by Hochman, and study some related phenomena.
Citation: Magnus Aspenberg, Fredrik Ekström, Tomas Persson, Jörg Schmeling. On the asymptotics of the scenery flow. Discrete & Continuous Dynamical Systems - A, 2015, 35 (7) : 2797-2815. doi: 10.3934/dcds.2015.35.2797
##### References:
 [1] C. Bandt, The Tangent Distribution for Self-Similar Measures,, Lecture at the 5th Conference on Real Analysis and Measure Theory, (1992).   Google Scholar [2] K. Falconer, Techniques in Fractal Geometry,, John Wiley & sons, (1997).   Google Scholar [3] M. Gavish, Measures with uniform scaling scenery,, Ergod. Th. & Dynam. Sys., 31 (2011), 33.  doi: 10.1017/S0143385709000996.  Google Scholar [4] S. Graf, On Bandt's tangential distribution for self-similar measures,, Monatsh. Math., 120 (1995), 223.  doi: 10.1007/BF01294859.  Google Scholar [5] M. Hochman, Geometric rigidity of $\times m$ invariant measures,, J. Eur. Math. Soc., 14 (2012), 1539.  doi: 10.4171/JEMS/340.  Google Scholar [6] M. Hochman, Dynamics on fractals and fractal distributions,, preprint, (2013).   Google Scholar [7] M. Hochman, Erratum to "Geometric rigidity of $\times m$ invariant measures'',, J. Eur. Math. Soc., 15 (2013), 2463.  doi: 10.4171/JEMS/425.  Google Scholar [8] D. W. Stroock, Probability Theory, an Analytic View,, Cambridge University Press, (1993).   Google Scholar

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##### References:
 [1] C. Bandt, The Tangent Distribution for Self-Similar Measures,, Lecture at the 5th Conference on Real Analysis and Measure Theory, (1992).   Google Scholar [2] K. Falconer, Techniques in Fractal Geometry,, John Wiley & sons, (1997).   Google Scholar [3] M. Gavish, Measures with uniform scaling scenery,, Ergod. Th. & Dynam. Sys., 31 (2011), 33.  doi: 10.1017/S0143385709000996.  Google Scholar [4] S. Graf, On Bandt's tangential distribution for self-similar measures,, Monatsh. Math., 120 (1995), 223.  doi: 10.1007/BF01294859.  Google Scholar [5] M. Hochman, Geometric rigidity of $\times m$ invariant measures,, J. Eur. Math. Soc., 14 (2012), 1539.  doi: 10.4171/JEMS/340.  Google Scholar [6] M. Hochman, Dynamics on fractals and fractal distributions,, preprint, (2013).   Google Scholar [7] M. Hochman, Erratum to "Geometric rigidity of $\times m$ invariant measures'',, J. Eur. Math. Soc., 15 (2013), 2463.  doi: 10.4171/JEMS/425.  Google Scholar [8] D. W. Stroock, Probability Theory, an Analytic View,, Cambridge University Press, (1993).   Google Scholar
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