Transversality for Critical Relations of Families of Rational Maps: An Elementary Proof

DOI10.1007/978-3-030-16833-9_11zbMath1446.37047arXiv1702.02582OpenAlexW2594424083WikidataQ128281312 ScholiaQ128281312MaRDI QIDQ3296168

Wei Xiao Shen, Genadi Levin, Sebastian J. van Strien

Publication date: 7 July 2020

Published in: New Trends in One-Dimensional Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.02582

zbMATH Keywords

transversalityrational mapsholomorphic dynamics

Mathematics Subject Classification ID

Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Combinatorics and topology in relation with holomorphic dynamical systems (37F20) Critical orbits for holomorphic dynamical systems (37F12)

Related Items (5)

Monotonicity of entropy for unimodal real quadratic rational maps ⋮ Moduli spaces for dynamical systems with portraits ⋮ Positive transversality via transfer operators and holomorphic motions with applications to monotonicity for interval maps ⋮ Zalcman functions and similarity between the Mandelbrot set, Julia sets, and the tricorn ⋮ Transversality in the setting of hyperbolic and parabolic maps

Cites Work

• Dynamical properties of some classes of entire functions
• Distribution of postcritically finite polynomials
• Amenability, Poincaré series and quasiconformal maps
• A Ruelle operator for a real Julia set
• Complex dynamics
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• Rational functions with real critical points and the B. and M. Shapiro conjecture in real enumerative geometry
• On entropy and monotonicity for real cubic maps (with an appendix by Adrien Douady and Pierrette Sentenac)
• On an analytic approach to the Fatou conjecture
• Perturbations of weakly expanding critical orbits
• Multipliers of periodic orbits in spaces of rational maps
• A Markov-type inequality for arbitrary plane continua
• A simple proof for monotonicity of entropy in the quadratic family
• Dynamics of post-critically finite maps in higher dimension
• Remarks on the Ruelle operator and the invariant line fields problem: II
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