Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T04:06:05.040Z Has data issue: false hasContentIssue false
  • English
  • Français

The flat-trace asymptotics of a uniform system of contractions

Published online by Cambridge University Press:  14 October 2010

David Fried
David Fried
Affiliation:
Dept of Mathematics, Boston University, III Cummington St, Boston, MA 02215, USA
Get access Rights & Permissions [Opens in a new window]

Extract

We develop a variant of the Taylor approximation approach to the periodic points of systems of contraction mappings [Rl] that does not invoke compactness conditions. Our presentation is simpler, in that certain steps are bypassed and only one basic estimate is used (Lemma 1). We also study the distribution of the discrete spectrum for the relevant transfer operators (Proposition 2).

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 6 , December 1995 , pp. 1061 - 1073
Copyright
Copyright © Cambridge University Press 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[AB]Atiyah, M. and Bott, R.. Notes on the Lefschetz fixed point theorem for elliptic complexes. Harvard, 1964.Google Scholar
[CHM]Chowla, S., Herstein, I. N. and Moore, W. K.. On recursions connected with symmetric groups. I. Can. J. Math. 3 (1951), 328–334.CrossRefGoogle Scholar
[Fl]Fried, D.. Zeta functions of Ruelle and Selberg 1. Ann. Sci. E.N.S. 19 (1986), 491–517.Google Scholar
[F2]Fried, D.. Symbolic dynamics for triangle groups. To appear in Inv. Math.Google Scholar
[F3]Fried, D.. Lefschetz formulas for flows. Lefschetz Centennial Conference proceedings. Contemp. Math. 58 111 (1987), 19–69.CrossRefGoogle Scholar
[G]Grothendieck, A.. La theorie de Fredholm. Bull. Soc. Math. France 84 (1956), 319–384.CrossRefGoogle Scholar
[GS]Guillemin, V. and Sternberg, S.. Geometric Asymptotics. AMS Math. Surveys 14, 1978.CrossRefGoogle Scholar
[M]Mayer, D.. On the thermodynamic formalism for the Gauss map. Commun. Math. Phys. 130 (1990), 311–333.Google Scholar
[Na]Nash, J.. The embedding problem for Riemann manifolds. Ann. Math. 63 (1956), 20–63.CrossRefGoogle Scholar
[N]Nussbaum, R.. The radius of the essential spectrum. Duke Math J. 37 (1970), 473–478.CrossRefGoogle Scholar
[Rl]Ruelle, D.. An extension of the theory of Fredholm determinants. Publ. Math IHES 72 (1990), 175–193.CrossRefGoogle Scholar
[R2]Ruelle, D.. Zeta functions for expanding maps and Anosov flows. Inv. Math. 34 (1976), 231–242.CrossRefGoogle Scholar
[Rus]Ruston, A. F.. On the Fredholm theory of integral equations for operators belonging to the trace class of a general Banach space. Proc. London. Math. Soc. 53 (2) (1951), 109–124.CrossRefGoogle Scholar
[S]Simon, B.. Trace Ideals and their Applications. LMS Lecture Notes 35. Cambridge University Press, Cambridge, 1979.Google Scholar
[Sm]Smithies, F.. The Fredholm theory of integral equations. Duke Math. J. 8 (1941), 107–130.CrossRefGoogle Scholar
[T]Tangerman, F.. Meromorphic continuation of Ruelle zeta functions. Thesis, Boston University, 1986.Google Scholar