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A Central Limit Theorem for linear combinations of iterates of an inner function is proved. The main technical tool is Aleksandrov Desintegration Theorem for Aleksandrov-Clark measures.
26 pages
Classificació AMS::37 Dynamical systems and ergodic theory::37A Ergodic theory, Dynamical aspects of measure-preserving transformations, central limit theorem, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica::Funcions de variable complexa, Ergodic theory, Teoria ergòdica, Functions, and related topics, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Differentiable dynamical systems, Complex Variables (math.CV), Inner functions, Central Limit Theorem, Entire, Aleksandrov-Clark measures, Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics, Mathematics - Complex Variables, Inner functions of one complex variable, Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable, inner functions, Sistemes dinàmics diferenciables, Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets, Classificació AMS::30 Functions of a complex variable::30D Entire and meromorphic functions, Funcions enteres, Mathematics - Classical Analysis and ODEs, 30J05, Classificació AMS::30 Functions of a complex variable::30D Entire and meromorphic functions, and related topics, Classificació AMS::37 Dynamical systems and ergodic theory::37F Complex dynamical systems, Functions, Entire
Classificació AMS::37 Dynamical systems and ergodic theory::37A Ergodic theory, Dynamical aspects of measure-preserving transformations, central limit theorem, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica::Funcions de variable complexa, Ergodic theory, Teoria ergòdica, Functions, and related topics, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Differentiable dynamical systems, Complex Variables (math.CV), Inner functions, Central Limit Theorem, Entire, Aleksandrov-Clark measures, Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics, Mathematics - Complex Variables, Inner functions of one complex variable, Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable, inner functions, Sistemes dinàmics diferenciables, Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets, Classificació AMS::30 Functions of a complex variable::30D Entire and meromorphic functions, Funcions enteres, Mathematics - Classical Analysis and ODEs, 30J05, Classificació AMS::30 Functions of a complex variable::30D Entire and meromorphic functions, and related topics, Classificació AMS::37 Dynamical systems and ergodic theory::37F Complex dynamical systems, Functions, Entire
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