Dynamics of transcendental Hénon maps
Sign Up to like & getrecommendations! Published in 2019 at "Mathematische Annalen"
DOI: 10.1007/s00208-018-1643-6
Abstract: The dynamics of transcendental functions in the complex plane has received a significant amount of attention. In particular much is known about the description of Fatou components. Besides the types of periodic Fatou components that… read more here.
Keywords: transcendental non; non maps; fatou components; dynamics transcendental ... See more keywords
Horn maps of semi-parabolic Hénon maps
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DOI: 10.1007/s00208-024-03085-3
Abstract: We prove that horn maps associated to quadratic semi-parabolic fixed points of Hénon maps, first introduced by Bedford, Smillie, and Ueda, satisfy a weak form of the Ahlfors island property. As a consequence, two natural… read more here.
Keywords: semi parabolic; horn maps; non maps; usepackage ... See more keywords
Symbolic dynamics for Hénon maps near the boundary of the horseshoe locus
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DOI: 10.1017/etds.2024.34
Abstract: Abstract Bedford and Smillie [A symbolic characterization of the horseshoe locus in the Hénon family. Ergod. Th. & Dynam. Sys. 37(5) (2017), 1389–1412] classified the dynamics of the Hénon map $f_{a, b} : (x, y)\mapsto… read more here.
Keywords: boundary horseshoe; horseshoe locus; non maps; symbolic dynamics ... See more keywords
More on the concept of anti-integrability for Hénon maps
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DOI: 10.1063/5.0280115
Abstract: For the family of Hénon maps (x,y)↦(a(1−x2)−by,x) of R2, the so-called anti-integrable (AI) limit concerns the limit a → ∞ with fixed Jacobian b. At the AI limit, the dynamics reduces to a subshift of… read more here.
Keywords: non maps; concept anti; integrability non; anti integrability ... See more keywords
Julia sets of complex Hénon maps
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DOI: 10.1142/s0129167x18500477
Abstract: There are two natural definitions of the Julia set for complex Henon maps: the sets J and J⋆. Whether these two sets are always equal is one of the main open questions in the field. We prove… read more here.
Keywords: complex non; julia sets; sets complex; non maps ... See more keywords