Thermodynamic formalism methods in the theory of iteration of mappings in dimension one, real and complex. (English) Zbl 1476.37053
This survey is focused on the application of thermodynamic formalism to hyperbolic and non-hyperbolic dynamics. In particular, the Hausdorff dimension and the Lyapunov exponents are two main topics of this contribution.
Reviewer: Tao Chen (New York)
MSC:
| 37D35 | Thermodynamic formalism, variational principles, equilibrium states for dynamical systems |
| 37E05 | Dynamical systems involving maps of the interval |
| 37F10 | Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets |
| 37F15 | Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems |
| 37F35 | Conformal densities and Hausdorff dimension for holomorphic dynamical systems |
| 31A20 | Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions |
Keywords:
one-dimensional dynamics; geometric pressure; thermodynamic formalism; equilibrium states; Hausdorff dimension; Lyapunov exponentsReferences:
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