Dynamics of the family 𝜆tan𝑧

DOI10.1090/S1088-4173-97-00017-9zbMath0884.30019arXivmath/9507225OpenAlexW1700084322WikidataQ115181070 ScholiaQ115181070MaRDI QIDQ4373810

Janina Kotus, Linda Keen

Publication date: 21 January 1998

Published in: Conformal Geometry and Dynamics of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9507225

zbMATH Keywords

iterationJulia setmeromorphic functionholomorphic motionparameter planetangent

Mathematics Subject Classification ID

Topological dynamics (37B99) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50) Dynamical systems over complex numbers (37F99)

Related Items (31)

A study of a meromorphic perturbation of the sine family ⋮ Iteration of quasiregular tangent functions in three dimensions ⋮ DYNAMICS OF THE FAMILY tan z2 ⋮ COMBINATORIAL STRUCTURE OF THE PARAMETER PLANE OF THE FAMILY λ tan z2 ⋮ Totally disconnected Julia set for different classes of meromorphic functions ⋮ Accessible boundary points in the shift locus of a family of meromorphic functions with two finite asymptotic values ⋮ Dynamics of a family of transcendental meromorphic functions having rational Schwarzian derivative ⋮ Parametrized dynamics of the Weierstrass elliptic function ⋮ Cantor and connected Julia sets of the parameterized Dixon elliptic functions ⋮ On the viscosity approximation type iterative method and its non-linear behaviour in the generation of Mandelbrot and Julia sets ⋮ Slices of parameter space for meromorphic maps with two asymptotic values ⋮ On Fatou sets containing Baker omitted value ⋮ Non-ergodic maps in the tangent family ⋮ Dynamics of Some Nonlinear Meromorphic Functions ⋮ Cycle doubling, merging, and renormalization in the tangent family ⋮ Iteration of certain meromorphic functions with unbounded singular values ⋮ Elliptic functions with critical orbits approaching infinity ⋮ Cantor Julia sets in a family of even elliptic functions ⋮ Misiurewicz parameters in the exponential family ⋮ Geometric rigidity of transcendental meromorphic functions ⋮ Iteration of the translated tangent ⋮ Stable components in the parameter plane of transcendental functions of finite type ⋮ Siegel disks of the tangent family ⋮ The Picard-Mann iteration with \(s\)-convexity in the generation of Mandelbrot and Julia sets ⋮ Parameter rays in the space of exponential maps ⋮ Dynamics of the meromorphic families $f_\lambda=\lambda \tan^pz^q$ ⋮ PARAMETERIZED DYNAMICS FOR THE WEIERSTRASS ELLIPTIC FUNCTION OVER SQUARE PERIOD LATTICES ⋮ A fundamental dichotomy for Julia sets of a family of elliptic functions ⋮ Mandelbrot-like set for some family of transcendental meromorphic functions ⋮ Fixed points, symmetries, and bounds for basins of attraction of complex trigonometric functions ⋮ Lyapunov exponents for non-ergodic meromorphic functions

Cites Work

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• On the dynamics of rational maps
• Iterates of Meromorphic Functions II: Examples of Wandering Domains
• Iterates of meromorphic functions: I
• Dynamics of exp (z)
• Dynamics of meromorphic maps : maps with polynomial schwarzian derivative
• Iterates of meromorphic functions III: Preperiodic domains
• Frontiers in complex dynamics

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