scholarly journals Absolutely continuous invariant measures for some piecewise hyperbolic affine maps – CORRIGENDUM

2021 ◽  
pp. 1-1
Author(s):  
TOMAS PERSSON
Keyword(s):  
Invariant Measures ◽  
Absolutely Continuous ◽  
Absolutely Continuous Invariant Measures ◽  
Affine Maps ◽  
Absolutely Continuous Invariant

scholarly journals Absolutely continuous invariant measures for some piecewise hyperbolic affine maps

2008 ◽  
Vol 28 (1) ◽  
pp. 211-228 ◽  
Author(s):  
TOMAS PERSSON
Keyword(s):  
Invariant Measure ◽  
Invariant Measures ◽  
Bounded Subset ◽  
Continuous Invariant Measure ◽  
Absolutely Continuous ◽  
Absolutely Continuous Invariant Measures ◽  
Piecewise Affine ◽  
Affine Maps ◽  
Absolutely Continuous Invariant Measure ◽  
Absolutely Continuous Invariant

AbstractA class of piecewise affine hyperbolic maps on a bounded subset of the plane is considered. It is shown that if a map from this class is sufficiently area-expanding then almost surely this map has an absolutely continuous invariant measure.

scholarly journals Multidimensional expanding maps with singularities: a pedestrian approach

2012 ◽  
Vol 33 (1) ◽  
pp. 168-182 ◽  
Author(s):  
CARLANGELO LIVERANI
Keyword(s):  
Invariant Measures ◽  
Statistical Properties ◽  
Expanding Maps ◽  
Absolutely Continuous ◽  
Absolutely Continuous Invariant Measures ◽  
Basic Properties ◽  
Bv Functions ◽  
Absolutely Continuous Invariant ◽  
Functions Of Bounded Variations ◽  
Bounded Derivative

AbstractI provide a proof of the existence of absolutely continuous invariant measures (and study their statistical properties) for multidimensional piecewise expanding systems with not necessarily bounded derivative or distortion. The proof uses basic properties of multidimensional BV functions (the space of functions of bounded variations).

scholarly journals Absolutely continuous invariant measures for non-uniformly expanding maps

2009 ◽  
Vol 29 (4) ◽  
pp. 1185-1215 ◽  
Author(s):  
HUYI HU ◽  
SANDRO VAIENTI
Keyword(s):  
Invariant Measure ◽  
Fixed Points ◽  
Large Class ◽  
Invariant Measures ◽  
Continuous Invariant Measure ◽  
Expanding Maps ◽  
Absolutely Continuous ◽  
Absolutely Continuous Invariant Measures ◽  
Absolutely Continuous Invariant Measure ◽  
Absolutely Continuous Invariant

AbstractFor a large class of non-uniformly expanding maps of ℝm, with indifferent fixed points and unbounded distortion and that are non-necessarily Markovian, we construct an absolutely continuous invariant measure. We extend previously used techniques for expanding maps on quasi-Hölder spaces to our case. We give general conditions and provide examples to which our results apply.

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