Fredholm determinants for hyperbolic diffeomorphisms of finite smoothness
Abstract
Given a map 0951-7715/12/1/008/img1 and a function 0951-7715/12/1/008/img2, a `Fredholm determinant' can be defined as a formal power series 0951-7715/12/1/008/img3. The coefficients 0951-7715/12/1/008/img4 are related to the periodic points of 0951-7715/12/1/008/img5. Assume that 0951-7715/12/1/008/img5 is a hyperbolic diffeomorphism of class 0951-7715/12/1/008/img7, and 0951-7715/12/1/008/img8 belongs to 0951-7715/12/1/008/img9. Then the Fredholm determinant is analytic in the disc of radius 0951-7715/12/1/008/img10, where 0951-7715/12/1/008/img11 is a hyperbolicity index of 0951-7715/12/1/008/img5 (roughly speaking, 0951-7715/12/1/008/img5 is 0951-7715/12/1/008/img14-contracting in one direction and 0951-7715/12/1/008/img15-expanding in the other direction). In the 0951-7715/12/1/008/img16 case, the Fredholm determinant is an entire function.
- Publication:
-
Nonlinearity
- Pub Date:
- January 1999
- DOI:
- 10.1088/0951-7715/12/1/008
- Bibcode:
- 1999Nonli..12..141K