Bowen-Ruelle measures for certain piecewise hyperbolic maps
Bowen-Ruelle measures for certain piecewise hyperbolic maps
We consider a class of piecewise <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C squared"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{C^2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> Lozi-like maps and prove the existence of invariant measures with absolutely continuous conditional measures on unstable manifolds