2 results
Recurrence to Shrinking Targets on Typical Self-Affine Fractals
- Part of
-
- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 61 / Issue 2 / May 2018
- Published online by Cambridge University Press:
- 15 February 2018, pp. 387-400
-
- Article
- Export citation
ITERATED LOGARITHM SPEED OF RETURN TIMES
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 96 / Issue 3 / December 2017
- Published online by Cambridge University Press:
- 04 October 2017, pp. 468-478
- Print publication:
- December 2017
-
- Article
-
- You have access
- Export citation
-
In a general setting of an ergodic dynamical system, we give a more accurate calculation of the speed of the recurrence of a point to itself (or to a fixed point). Precisely, we show that for a certain
$\unicode[STIX]{x1D709}$ depending on the dimension of the space, 
$\liminf _{n\rightarrow +\infty }(n\log \log n)^{\unicode[STIX]{x1D709}}d(T^{n}x,x)=0$ almost everywhere and 
$\liminf _{n\rightarrow +\infty }(n\log \log n)^{\unicode[STIX]{x1D709}}d(T^{n}x,y)=0$ for almost all 
$x$ and 
$y$. This is done by assuming the exponential decay of correlations and making a weak assumption on the invariant measure.
