summability condition
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2013 ◽  
Vol 89 (2) ◽  
pp. 308-315
Author(s):  
HUAIBIN LI

AbstractConsider a map of class ${C}^{3} $ with nonflat critical points and with all periodic points hyperbolic repelling. We show that the ‘backward contracting condition’ implies the summability condition. This result is the converse of Theorem 3 of Bruin et al. [‘Large derivatives, backward contraction and invariant densities for interval maps’, Invent. Math. 172 (2008), 509–533].


2013 ◽  
Vol 34 (4) ◽  
pp. 1184-1209 ◽  
Author(s):  
BING GAO ◽  
WEIXIAO SHEN

AbstractWe provide a strengthened version of the famous Jakobson's theorem. Consider an interval map $f$ satisfying a summability condition. For a generic one-parameter family ${f}_{t} $ of maps with ${f}_{0} = f$, we prove that $t= 0$ is a Lebesgue density point of the set of parameters for which ${f}_{t} $ satisfies both the Collet–Eckmann condition and a strong polynomial recurrence condition.


1991 ◽  
Vol 105 (1) ◽  
pp. 123-136 ◽  
Author(s):  
Tomasz Nowicki ◽  
Sebastian van Strien

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