Ergodic theory and dynamical systems, ISSN 0143-3857, 08/2012, Volume 32, Issue 4, pp. 1165 - 1189

Let f be an arbitrary transcendental entire or meromorphic function in the class...

HAUSDORFF DIMENSION | JULIA SETS | MATHEMATICS | MATHEMATICS, APPLIED | REAL ANALYTICITY | DYNAMICS | FORMALISM | GEOMETRY | Singularities | Infimum | Meromorphic functions | Topology | Dynamical systems | Closures | Invariants | Ergodic processes | Mathematics - Dynamical Systems

HAUSDORFF DIMENSION | JULIA SETS | MATHEMATICS | MATHEMATICS, APPLIED | REAL ANALYTICITY | DYNAMICS | FORMALISM | GEOMETRY | Singularities | Infimum | Meromorphic functions | Topology | Dynamical systems | Closures | Invariants | Ergodic processes | Mathematics - Dynamical Systems

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 2011, Volume 250, Issue 2, pp. 487 - 509

Following the definition of parabolic rational functions and in view of the behavior of transcendental meromorphic functions, we give the definition of parabolic transcendental meromorphic functions...

Parabolic meromorphic functions | Conformal measures | Expansive map | Poincaré exponents | Pressure functions | JULIA SETS | MATHEMATICS | ITERATION | INVARIANT-MEASURES | expansive map | parabolic meromorphic functions | pressure functions | RATIONAL MAPS | conformal measures | Poincare exponents

Parabolic meromorphic functions | Conformal measures | Expansive map | Poincaré exponents | Pressure functions | JULIA SETS | MATHEMATICS | ITERATION | INVARIANT-MEASURES | expansive map | parabolic meromorphic functions | pressure functions | RATIONAL MAPS | conformal measures | Poincare exponents

Journal Article

Research in the Mathematical Sciences, ISSN 2522-0144, 3/2019, Volume 6, Issue 1, pp. 1 - 34

Using the locally compact abelian group $$\mathbb {T}\times \mathbb {Z}$$ T×Z , we assign a meromorphic function to each ideal triangulation of a 3-manifold with torus boundary components...

Ideal triangulations | 3-manifolds | Computational Mathematics and Numerical Analysis | Quantum dilogarithm | State integrals | Mathematics, general | Mathematics | 3D index | Meromorphic functions | Applications of Mathematics | Locally compact abelian groups | MATHEMATICS | TQFT

Ideal triangulations | 3-manifolds | Computational Mathematics and Numerical Analysis | Quantum dilogarithm | State integrals | Mathematics, general | Mathematics | 3D index | Meromorphic functions | Applications of Mathematics | Locally compact abelian groups | MATHEMATICS | TQFT

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2012, Volume 394, Issue 2, pp. 458 - 467

We prove some results concerning the possible configurations of Herman rings for transcendental meromorphic functions...

Herman rings | Configuration | Complex dynamical systems | Fatou set | Julia set | Quasiconformal surgery | Invariant curves | MATHEMATICS | MATHEMATICS, APPLIED | EXAMPLES | DOMAINS | Ergodic theory | Functions of complex variables | Teoria ergòdica | Funcions de variables complexes

Herman rings | Configuration | Complex dynamical systems | Fatou set | Julia set | Quasiconformal surgery | Invariant curves | MATHEMATICS | MATHEMATICS, APPLIED | EXAMPLES | DOMAINS | Ergodic theory | Functions of complex variables | Teoria ergòdica | Funcions de variables complexes

Journal Article

Houston Journal of Mathematics, ISSN 0362-1588, 2013, Volume 39, Issue 4, pp. 1149 - 1159

For a parabolic meromorphic function on the Riemann sphere, we proved the existence of s-conformal measure and gave a sufficient condition for the existence of the invariant measure equivalent...

Poincaré Exponents | Conformal measures | Parabolic Meromorphic functions | Invariant measure | MATHEMATICS | Poincare Exponents | HAUSDORFF | SYSTEMS | GEOMETRICALLY FINITE | RATIONAL MAPS

Poincaré Exponents | Conformal measures | Parabolic Meromorphic functions | Invariant measure | MATHEMATICS | Poincare Exponents | HAUSDORFF | SYSTEMS | GEOMETRICALLY FINITE | RATIONAL MAPS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2008, Volume 340, Issue 2, pp. 954 - 958

If a transcendental meromorphic function f with finitely many poles has a completely invariant domain U which is simply connected and satisfies some conditions, we prove F ( f ) = U...

Completely invariant domain | Logarithmic singularity | ogarithmic singularity | MATHEMATICS | ITERATION | MATHEMATICS, APPLIED | SETS | WANDERING DOMAINS | completely invariant domain

Completely invariant domain | Logarithmic singularity | ogarithmic singularity | MATHEMATICS | ITERATION | MATHEMATICS, APPLIED | SETS | WANDERING DOMAINS | completely invariant domain

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2009, Volume 357, Issue 1, pp. 244 - 253

A version of the second main theorem of Nevanlinna theory is proved, where the ramification term is replaced by a term depending on a certain composition operator of a meromorphic function of small hyper-order...

Picard's theorem | Forward invariant | Value distribution | Second main theorem | Hyper-order | MATHEMATICS | MATHEMATICS, APPLIED | OPERATOR | DIFFERENCE-EQUATIONS | NEVANLINNA THEORY | Mathematics - Complex Variables

Picard's theorem | Forward invariant | Value distribution | Second main theorem | Hyper-order | MATHEMATICS | MATHEMATICS, APPLIED | OPERATOR | DIFFERENCE-EQUATIONS | NEVANLINNA THEORY | Mathematics - Complex Variables

Journal Article

Journal d'Analyse Mathématique, ISSN 0021-7670, 1/2011, Volume 113, Issue 1, pp. 305 - 329

.... We prove that if a smooth and regular (in a certain sense) function f in Ω = ∪C t , possesses, for each t ∈ (0, 1...

Abstract Harmonic Analysis | Mathematics | Functional Analysis | Dynamical Systems and Ergodic Theory | Analysis | Partial Differential Equations | MATHEMATICS | ROTATION INVARIANT FAMILIES | STRIP | TESTING ANALYTICITY | CR FOLIATIONS | CURVES

Abstract Harmonic Analysis | Mathematics | Functional Analysis | Dynamical Systems and Ergodic Theory | Analysis | Partial Differential Equations | MATHEMATICS | ROTATION INVARIANT FAMILIES | STRIP | TESTING ANALYTICITY | CR FOLIATIONS | CURVES

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 05/2015, Volume 35, Issue 5, pp. 2273 - 2298

A definition of hyperbolic meromorphic functions is given and then we discuss the dynamical behavior and the thermodynamic formalism of hyperbolic functions on their Julia sets...

Hausdorff dimension | Bowen formula | Conformal measures | Hyperbolic meromorphic functions | ITERATION | MATHEMATICS, APPLIED | SINGULARITIES | conformal measures | JULIA SETS | FUNCTIONS II | MATHEMATICS | EXPONENTIAL FAMILY | INVARIANT-MEASURES | MAPS | LIMIT FUNCTIONS

Hausdorff dimension | Bowen formula | Conformal measures | Hyperbolic meromorphic functions | ITERATION | MATHEMATICS, APPLIED | SINGULARITIES | conformal measures | JULIA SETS | FUNCTIONS II | MATHEMATICS | EXPONENTIAL FAMILY | INVARIANT-MEASURES | MAPS | LIMIT FUNCTIONS

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 10/2006, Volume 279, Issue 13‐14, pp. 1565 - 1584

The meromorphic maps f(lambda) (z) = lambda (1 - exp (- 2 z))(-1), lambda > 0, of the complex plane are thoroughly investigated. With each map f(lambda...

invariant measure | Hausdorff dimension | packing measure | Julia set | Meromorphic function | Packing measure | Invariant measure | EXISTENCE | ELLIPTIC FUNCTIONS | JULIA SETS | MATHEMATICS | INDIFFERENT PERIODIC POINT | EXPONENTIAL FAMILY | INVARIANT-MEASURES | CONFORMAL MEASURES | meromorphic function | ERGODIC-THEORY | RATIONAL MAPS

invariant measure | Hausdorff dimension | packing measure | Julia set | Meromorphic function | Packing measure | Invariant measure | EXISTENCE | ELLIPTIC FUNCTIONS | JULIA SETS | MATHEMATICS | INDIFFERENT PERIODIC POINT | EXPONENTIAL FAMILY | INVARIANT-MEASURES | CONFORMAL MEASURES | meromorphic function | ERGODIC-THEORY | RATIONAL MAPS

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 04/1993, Volume 153, Issue 1, pp. 159 - 185

.... In this paper all meromorphic modular invariant combinations of the allowed Kac-Moody combinations are obtained...

VIRASORO ALGEBRAS | STRING MODELS | GENERAL INDEXES | SIMPLE CURRENTS | EXPLICIT PROOF | BRANCHING-RULES | INVARIANT PARTITION-FUNCTIONS | KAC-MOODY ALGEBRAS | MODULAR INVARIANTS | PHYSICS, MATHEMATICAL | 2 DIMENSIONS | Physics - High Energy Physics - Theory | 17B67 | 81T40 | 81R10 | 11F22

VIRASORO ALGEBRAS | STRING MODELS | GENERAL INDEXES | SIMPLE CURRENTS | EXPLICIT PROOF | BRANCHING-RULES | INVARIANT PARTITION-FUNCTIONS | KAC-MOODY ALGEBRAS | MODULAR INVARIANTS | PHYSICS, MATHEMATICAL | 2 DIMENSIONS | Physics - High Energy Physics - Theory | 17B67 | 81T40 | 81R10 | 11F22

Journal Article

Ergodic theory and dynamical systems, ISSN 0143-3857, 10/2012, Volume 32, Issue 5, pp. 1691 - 1710

.... This proof applies not only to rational and transcendental meromorphic functions (where it was previously known...

JULIA SETS | MATHEMATICS | DYNAMICS | MATHEMATICS, APPLIED | DIMENSION | Variables | Islands | Maps | Mathematical analysis | Proving | Differentials | Rigidity | Dynamical systems | Invariants

JULIA SETS | MATHEMATICS | DYNAMICS | MATHEMATICS, APPLIED | DIMENSION | Variables | Islands | Maps | Mathematical analysis | Proving | Differentials | Rigidity | Dynamical systems | Invariants

Journal Article

Journal d'Analyse Mathématique, ISSN 0021-7670, 2/2018, Volume 134, Issue 1, pp. 201 - 235

This work concerns random dynamics of hyperbolic entire and meromorphic functions of finite order whose derivative satisfies some growth condition...

Abstract Harmonic Analysis | Mathematics | Functional Analysis | Dynamical Systems and Ergodic Theory | Analysis | Partial Differential Equations | THERMODYNAMIC FORMALISM | MATHEMATICS | SEMIGROUPS | DIMENSIONS | SYSTEMS | THEOREM | Operators (mathematics) | Transcendental functions | Meromorphic functions | Cones | Invariants

Abstract Harmonic Analysis | Mathematics | Functional Analysis | Dynamical Systems and Ergodic Theory | Analysis | Partial Differential Equations | THERMODYNAMIC FORMALISM | MATHEMATICS | SEMIGROUPS | DIMENSIONS | SYSTEMS | THEOREM | Operators (mathematics) | Transcendental functions | Meromorphic functions | Cones | Invariants

Journal Article

Discrete and Continuous Dynamical Systems - Series B, ISSN 1531-3492, 01/2015, Volume 20, Issue 1, pp. 249 - 257

.... These results extend Denker and Urbanski's work on parabolic rational functions.

Singular values | Hausdorff dimension | Conformal measures | Parabolic meromorphic function | Julia set | MATHEMATICS, APPLIED | INVARIANT-MEASURES | singular values | RATIONAL MAPS | conformal measures

Singular values | Hausdorff dimension | Conformal measures | Parabolic meromorphic function | Julia set | MATHEMATICS, APPLIED | INVARIANT-MEASURES | singular values | RATIONAL MAPS | conformal measures

Journal Article

Complex Variables and Elliptic Equations, ISSN 1747-6933, 10/2016, Volume 61, Issue 10, pp. 1353 - 1361

We define Baker omitted value, in short bov, of an entire or meromorphic function f in the complex plane as an omitted value for which there exists such that for each ball centred at a and...

entire function | completely invariant Fatou component | Baker wandering domain | meromorphic function | Omitted value | MATHEMATICS | MEROMORPHIC FUNCTIONS | 37F50 | 37F10 | 30D05 | Planes | Entire functions | Mathematical analysis | Images | Meromorphic functions | Complex variables | Boundaries | Invariants

entire function | completely invariant Fatou component | Baker wandering domain | meromorphic function | Omitted value | MATHEMATICS | MEROMORPHIC FUNCTIONS | 37F50 | 37F10 | 30D05 | Planes | Entire functions | Mathematical analysis | Images | Meromorphic functions | Complex variables | Boundaries | Invariants

Journal Article

Journal of Difference Equations and Applications, ISSN 1023-6198, 11/2017, Volume 23, Issue 11, pp. 1869 - 1883

Given a transcendental meromorphic function that satisfies an asymptotic behaviour near infinity, Rippon and Stallard showed that such function has a family of invariant Baker domains associated...

30D30 (primary) | Meromorphic functions | asymptotic representations | 30E15 (secondary) | Baker domains | Fatou set | ITERATION | MATHEMATICS, APPLIED | 37F10 | 30D05 | Singularities | Infinity | Mathematical analysis | Exact solutions | Closed form solutions | Invariants

30D30 (primary) | Meromorphic functions | asymptotic representations | 30E15 (secondary) | Baker domains | Fatou set | ITERATION | MATHEMATICS, APPLIED | 37F10 | 30D05 | Singularities | Infinity | Mathematical analysis | Exact solutions | Closed form solutions | Invariants

Journal Article

1978, Lecture notes in mathematics, ISBN 0387086595, Volume 637., vii, 194

Book

Tôhoku mathematical journal, ISSN 0040-8735, 2007, Volume 59, Issue 2, pp. 167 - 202

The main purpose of the present paper is to show that a class of dynamical zeta functions associated with the so-called two-dimensional open billiard without eclipse have meromorphic extensions...

dispersing billiards without eclipse | thermodynamic formalism | Dynamical zeta functions | Dispersing billiards without eclipse | Thermodynamic formalism | MATHEMATICS | dynamical zeta functions | DECAY | HYPERBOLIC BILLIARDS | INVARIANT | TRANSFORMATIONS

dispersing billiards without eclipse | thermodynamic formalism | Dynamical zeta functions | Dispersing billiards without eclipse | Thermodynamic formalism | MATHEMATICS | dynamical zeta functions | DECAY | HYPERBOLIC BILLIARDS | INVARIANT | TRANSFORMATIONS

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 10/2016, Volume 10, Issue 7, pp. 1619 - 1654

... ) -meromorphic functions. Some general versions of extension theorem of Levi type are extended to the classes of meromorphic functions f on $$D \times (\Delta _r {\setminus } \overline{\Delta })$$ D × ( Δ r \ Δ...

32B10 | 32A20 | Locally pluriregular set | 32A10 | 46E50 | Mathematics | Holomorphic functions | Meromorphic functions | 46A63 | Operator Theory | Plurisubharmonic functions | 46A04 | Analysis | Mathematics, general | Topological linear invariants | 32U05 | Pluripolar set | MATHEMATICS | MATHEMATICS, APPLIED | FRECHET SPACES | HOLOMORPHIC-FUNCTIONS

32B10 | 32A20 | Locally pluriregular set | 32A10 | 46E50 | Mathematics | Holomorphic functions | Meromorphic functions | 46A63 | Operator Theory | Plurisubharmonic functions | 46A04 | Analysis | Mathematics, general | Topological linear invariants | 32U05 | Pluripolar set | MATHEMATICS | MATHEMATICS, APPLIED | FRECHET SPACES | HOLOMORPHIC-FUNCTIONS

Journal Article

Annales de l'Institut Fourier, ISSN 0373-0956, 2012, Volume 62, Issue 5, pp. 1983 - 2011

In this paper we develop fundamental tools and methods to study meromorphic functions in an equivariant setup...

Rosenlicht quotient | Invariant meromorphic function | Stein space | Lie group action | MATHEMATICS | invariant meromorphic function | MANIFOLDS | ALGEBRAIC GROUPS | ABBILDUNGEN KOMPLEXER RAUME | REDUCTIVE GROUP | Mathematics - Complex Variables

Rosenlicht quotient | Invariant meromorphic function | Stein space | Lie group action | MATHEMATICS | invariant meromorphic function | MANIFOLDS | ALGEBRAIC GROUPS | ABBILDUNGEN KOMPLEXER RAUME | REDUCTIVE GROUP | Mathematics - Complex Variables

Journal Article

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