Exponential speed of mixing for skew-products with singularities

R Markarian, M J Pacifico, J L Vieitez
2012 Nonlinearity  
Let f: [0,1]× [0,1] ∖1/2→ [0,1]× [0,1] be the C^∞ endomorphism given by f(x,y)=(2x- [2x], y+ c/|x-1/2|- [y+ c/|x-1/2|]), where c is a positive real number. We prove that f is topologically mixing and if c>1/4 then f is mixing with respect to Lebesgue measure. Furthermore we prove that the speed of mixing is exponential.
doi:10.1088/0951-7715/26/1/269 fatcat:zbdmytvrr5bxfaggilcqxxctzq