Examples of expanding \(C^1\) maps having no \(\sigma\)-finite invariant measure equivalent to Lebesgue

Measure-preserving transformations (28D05) Dynamical systems involving maps of the interval (37E05) Nonsingular (and infinite-measure preserving) transformations (37A40) Invariant measures for infinite-dimensional dissipative dynamical systems (37L40)

Related Items (2)

Equilibrium states and SRB-like measures of \(C^1\)-expanding maps of the circle ⋮ Ergodic and Bernoulli properties of analytic maps of complex projective space

Cites Work

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Quadratic maps without asymptotic measure
Properties of fully developed chaos in one-dimensional maps
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Spectral theory, zeta functions and the distribution of periodic points for Collet-Eckmann maps
Sigma-finite invariant measures for smooth mappings of the circle
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Noninvertible Transformations Admitting no Absolutely Continuous σ- Finite Invariant Measure
Bounded variation and invariant measures
On a Bernoulli shift with non-identical factor measures
A Structure Theorem for n -to-1 Endomorphisms and Existence of Non-Recurrent Measures
Un exemple de transformation dilatante et C¹ par morceaux de l'intervalle, sans probabilité absolument continue invariante
On the Existence of Invariant Measures for Piecewise Monotonic Transformations
Examples of Natural Extensions of Nonsingular Endomorphisms
Properties of invariant measures for piecewise expanding one-dimensional transformations with summable oscillations of derivative
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On invariant measures for expanding differentiable mappings

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