Nice sets and invariant densities in complex dynamics

@article{Dobbs2010NiceSA,
  title={Nice sets and invariant densities in complex dynamics},
  author={N. Dobbs},
  journal={Mathematical Proceedings of the Cambridge Philosophical Society},
  year={2010},
  volume={150},
  pages={157 - 165}
}
  • N. Dobbs
  • Published 2010
  • Mathematics
  • Mathematical Proceedings of the Cambridge Philosophical Society
Abstract In complex dynamics, we construct a so-called nice set (one for which the first return map is Markov) around any point which is in the Julia set but not in the post-singular set, adapting a construction of Rivera–Letelier. This simplifies the study of absolutely continuous invariant measures. We prove a converse to a recent theorem of Kotus and Świątek, so for a certain class of meromorphic maps the absolutely continuous invariant measure is finite if and only if an integrability… Expand
17 Citations
Finer fractal geometry for analytic families of conformal dynamical systems
Perturbing Misiurewicz Parameters in the Exponential Family
Knobbly but nice
  • N. Dobbs
  • Mathematics
  • Ergodic Theory and Dynamical Systems
  • 2021
Dynamical rigidity of transcendental meromorphic functions
...
1
2
...

References

SHOWING 1-10 OF 26 REFERENCES
No finite invariant density for Misiurewicz exponential maps
A connecting lemma for rational maps satisfying a no-growth condition
Invariant measures for meromorphic Misiurewicz maps
  • J. Kotus, G. Swiatek
  • Mathematics
  • Mathematical Proceedings of the Cambridge Philosophical Society
  • 2008
Rigidity of Conformal Iterated Function Systems
On cusps and flat tops
On iterations of Misiurewicz's rational maps on the Riemann sphere
...
1
2
3
...