Fredholm determinants for hyperbolic diffeomorphisms of finite smoothness
Abstract
Given a map 09517715/12/1/008/img1 and a function 09517715/12/1/008/img2, a `Fredholm determinant' can be defined as a formal power series 09517715/12/1/008/img3. The coefficients 09517715/12/1/008/img4 are related to the periodic points of 09517715/12/1/008/img5. Assume that 09517715/12/1/008/img5 is a hyperbolic diffeomorphism of class 09517715/12/1/008/img7, and 09517715/12/1/008/img8 belongs to 09517715/12/1/008/img9. Then the Fredholm determinant is analytic in the disc of radius 09517715/12/1/008/img10, where 09517715/12/1/008/img11 is a hyperbolicity index of 09517715/12/1/008/img5 (roughly speaking, 09517715/12/1/008/img5 is 09517715/12/1/008/img14contracting in one direction and 09517715/12/1/008/img15expanding in the other direction). In the 09517715/12/1/008/img16 case, the Fredholm determinant is an entire function.
 Publication:

Nonlinearity
 Pub Date:
 January 1999
 DOI:
 10.1088/09517715/12/1/008
 Bibcode:
 1999Nonli..12..141K