Absolutely continuous invariant probability measures for arbitrary expanding piecewise $\mathbb{R}$-analytic mappings of the plane

By Jérôme Buzzi. Ergodic Theory and Dynamical Systems, 2000

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Good Banach spaces for piecewise hyperbolic maps via interpolation (2007, background): “This functional approach has been extended to higher dimensional piecewise expanding maps, under stronger assumptions (the counter-examples of Tsujii [30] and Buzzi [11] show that some additional assumption is necessary), by considering various functional spaces (see the work of Keller, Góra–Boyarsk”