Invariant measures for some one-dimensional attractors

M. V. Jacobson
1982 Ergodic Theory and Dynamical Systems  
Dedicated to the memory of V. M. Alexeyev to whom I shall always be grateful for his friendship and encouragement Abstract. We consider certain non-invertible maps of the square which are extensions of the quadratic maps of the interval and their small perturbations. We show that several maps of the type possess attractors which are not hyperbolic but have invariant measures similar to Bowen-Ruelle measures for hyperbolic attractors.
doi:10.1017/s0143385700001644 fatcat:qpx2jozacbduln7dxjjxxte7py