NORMAL FAMILIES OF BICOMPLEX HOLOMORPHIC FUNCTIONS

DOI10.1142/S0218348X09004314zbMath1230.30032arXiv0806.4403OpenAlexW2057776955MaRDI QIDQ3647657

Dominic Rochon, N. Sharma, Kuldeep Singh Charak

Publication date: 23 November 2009

Published in: Fractals (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.4403

zbMATH Keywords

Julia setFatou setnormal familiesbicomplex numberscomplex Clifford algebrasMontel theorembicomplex dynamics

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Normal functions of one complex variable, normal families (30D45) Clifford algebras, spinors (15A66)

Related Items (19)

Multicomplex hyperfunctions ⋮ Fractional multicomplex polynomials ⋮ The Cauchy-Kowalewski product for bicomplex holomorphic functions ⋮ The generalized M-J sets for bicomplex numbers ⋮ Complex Laplacian and derivatives of bicomplex functions ⋮ Harmonic morphisms and bicomplex manifolds ⋮ Conjugate complex harmonic functions ⋮ Counterexamples to bicomplex analogue of Bloch's principle and its converse ⋮ On holomorphic hypercomplex connections ⋮ Bicomplex analogue of Zalcman lemma ⋮ Unnamed Item ⋮ Generalization of the Gauss--Lucas theorem for bicomplex polynomials ⋮ Bernstein-type Inequalities for Bicomplex Polynomials ⋮ Singularities of functions of one and several bicomplex variables ⋮ Bicomplex hyperfunctions ⋮ The inverse iteration method for Julia sets in the 3-dimensional space ⋮ On anti-Hermitian metric connections preserving a bicomplex structure ⋮ ON A GENERALIZED FATOU–JULIA THEOREM IN MULTICOMPLEX SPACES ⋮ ON BICOMPLEX-HOLOMORPHIC MANIFOLDS

Cites Work

• A GENERALIZED MANDELBROT SET FOR BICOMPLEX NUMBERS
• Complexified clifford analysis
• Normal families: New perspectives
• On a Generalized Fatou-Julia Theorem
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