Zeta Functions and Asymptotic Formulae for Preperiodic Orbits of Hyperbolic Rational Maps
✍ Scribed by Simon Waddington
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 989 KB
- Volume
- 186
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
For a hyperbolic rational map R of the Riemann sphere of degree d 2 2, restricted to its . l d b set J(R), we define a %eta function C R ( d ) , which counts the prepenodic orbib of R, according to Lhe weight function IR'I : J(R) -+ C . An analysis of the analytic domain of ( ~( d ) , using techniques from symbolic dynamics, yields weighted asymptotic formulae for the preperiodic orbits of R. We describe m application to diophantine number theory. 1991 Mathemafica Subject Classification. Primary 30D05, Secondary 58320. Keywords and phrases. btional maps of the Riemann sphere, dynamical zeta functions.
Recently, the author haa obbined a more complete description of hypubolic mrp of types ( I ) md (1% P31