Nice Inducing Schemes and the Thermodynamics of Rational Maps

@article{Przytycki2008NiceIS,
  title={Nice Inducing Schemes and the Thermodynamics of Rational Maps},
  author={F. Przytycki and J. Rivera-Letelier},
  journal={Communications in Mathematical Physics},
  year={2008},
  volume={301},
  pages={661-707}
}
We study the thermodynamic formalism of a complex rational map f of degree at least two, viewed as a dynamical system acting on the Riemann sphere. More precisely, for a real parameter t we study the existence of equilibrium states of f for the potential $${-t {\rm ln} \left|f^{\prime} \right|}$$ , and the analytic dependence on t of the corresponding pressure function. We give a fairly complete description of the thermodynamic formalism for a large class of rational maps, including well known… Expand

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References

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On “Thermodynamics” of Rational MapsI.¶Negative Spectrum
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