Ellipticity of Operators Associated with Morse–Smale Diffeomorphisms

We consider the operator algebra generated by pseudodifferential operators on a closed smooth surface and shift operators induced by a Morse– Smale diffeomorphism of this surface. The elements of this algebra are considered as operators in the scale of Sobolev spaces, and the aim of this paper is to describe how the Fredholm property depends on the Sobolev smoothness exponent. © 2021, Springer Nature Switzerland AG.