Measures with positive Lyapunov exponent and conformal measures in rational dynamics

@article{Dobbs2008MeasuresWP,
  title={Measures with positive Lyapunov exponent and conformal measures in rational dynamics},
  author={N. Dobbs},
  journal={Transactions of the American Mathematical Society},
  year={2008},
  volume={364},
  pages={2803-2824}
}
  • N. Dobbs
  • Published 2008
  • Mathematics
  • Transactions of the American Mathematical Society
Ergodic properties of rational maps are studied, generalising the work of F. Ledrappier. A new construction allows for simpler proofs of stronger results. Very general conformal measures are considered. Equivalent conditions are given for an ergodic invariant probability measure with positive Lyapunov exponent to be absolutely continuous with respect to a general conformal measure. If they hold, we can construct an induced expanding Markov map with integrable return time which generates the… Expand
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  • 28
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  • 26
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  • 24
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  • 24
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  • 23
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References

SHOWING 1-10 OF 30 REFERENCES
Lyapunov characteristic exponents are nonnegative
  • 78
  • Highly Influential
  • PDF
Introduction to Ergodic theory
  • 1,584
  • PDF
A connecting lemma for rational maps satisfying a no-growth condition
  • 43
  • Highly Influential
  • PDF
On thermodynamics of rational maps on the Riemann sphere
  • 12
  • Highly Influential
  • PDF
Equality of pressures for rational functions
  • 38
Introduction to Ergodic Theory
  • 3,195
...
1
2
3
...