Inventiones mathematicae, ISSN 0020-9910, 12/2014, Volume 198, Issue 3, pp. 591 - 636

We prove that every transcendental meromorphic map $$f$$ f with disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of...

30D20 | Primary 30D05 | Mathematics, general | 37F10 | Mathematics | MATHEMATICS | ITERATION | NEWTONS METHOD | MAPS | DYNAMICS | BAKER DOMAINS | ANALYTIC-FUNCTIONS | Discs | Absorption | Mathematical analysis | Newton methods | Texts | Disks | Meromorphic functions | Boundaries | Mathematics - Dynamical Systems | Funcions enteres | Functions of complex variables | Entire functions | Funcions de variables complexes

30D20 | Primary 30D05 | Mathematics, general | 37F10 | Mathematics | MATHEMATICS | ITERATION | NEWTONS METHOD | MAPS | DYNAMICS | BAKER DOMAINS | ANALYTIC-FUNCTIONS | Discs | Absorption | Mathematical analysis | Newton methods | Texts | Disks | Meromorphic functions | Boundaries | Mathematics - Dynamical Systems | Funcions enteres | Functions of complex variables | Entire functions | Funcions de variables complexes

Journal Article

Proceedings of the London Mathematical Society, ISSN 0024-6115, 03/2019, Volume 118, Issue 3, pp. 701 - 728

Let f:M→M be a uniformly quasiregular self‐map of a compact, connected, and oriented Riemannian n‐manifold M without boundary, n⩾2. We show that, for...

30D05 (secondary) | 30C65 (primary) | 57M12 | MATHEMATICS | SYSTEMS | INTEGRABILITY | INEQUALITIES | SPACES

30D05 (secondary) | 30C65 (primary) | 57M12 | MATHEMATICS | SYSTEMS | INTEGRABILITY | INEQUALITIES | SPACES

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 07/2015, Volume 12, Issue 3, pp. 667 - 678

Journal Article

Bulletin of the London Mathematical Society, ISSN 0024-6093, 10/2018, Volume 50, Issue 5, pp. 916 - 932

The family of exponential maps fa(z)=ez+a is of fundamental importance in the study of transcendental dynamics. Here we consider the topological structure of...

30D05 | 54G15 (secondary) | 37F10 (primary) | JULIA SETS | HAUSDORFF DIMENSION | POLYNOMIALS | MATHEMATICS | ITERATION | EXPONENTIAL MAPS | HAIRS | DYNAMIC RAYS | TRANSCENDENTAL ENTIRE-FUNCTIONS | LAMBDA-EXP Z | GEOMETRY

30D05 | 54G15 (secondary) | 37F10 (primary) | JULIA SETS | HAUSDORFF DIMENSION | POLYNOMIALS | MATHEMATICS | ITERATION | EXPONENTIAL MAPS | HAIRS | DYNAMIC RAYS | TRANSCENDENTAL ENTIRE-FUNCTIONS | LAMBDA-EXP Z | GEOMETRY

Journal Article

Mathematische Annalen, ISSN 0025-5831, 12/2013, Volume 357, Issue 4, pp. 1577 - 1604

Let $$f$$ f be a real entire function whose set $$S(f)$$ S ( f ) of singular values is real and bounded. We show that, if $$f$$ f satisfies a certain...

Secondary 30D05 | Mathematics, general | Primary 37F10 | Mathematics | 30F45 | MATHEMATICS | ITERATION | MEROMORPHIC FUNCTIONS | MAPS | DIMENSION | DYNAMIC RAYS | BAKER

Secondary 30D05 | Mathematics, general | Primary 37F10 | Mathematics | 30F45 | MATHEMATICS | ITERATION | MEROMORPHIC FUNCTIONS | MAPS | DIMENSION | DYNAMIC RAYS | BAKER

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 12/2016, Volume 284, Issue 3, pp. 1053 - 1071

This article concerns the iteration of quasiregular mappings on $$\mathbb {R}^d$$ R d and entire functions on $$\mathbb {C}$$ C . It is shown that there are...

Secondary 30C65 | Mathematics, general | Primary 37F10 | 30D05 | Mathematics | MATHEMATICS | MAPS | FATOU | SETS | GROWTH | SPIDERS WEB | FIXED-POINTS

Secondary 30C65 | Mathematics, general | Primary 37F10 | 30D05 | Mathematics | MATHEMATICS | MAPS | FATOU | SETS | GROWTH | SPIDERS WEB | FIXED-POINTS

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 02/2020, Volume 70, Issue 1, pp. 81 - 86

Levels of fast escaping sets were discussed by Rippon and Stallard. Here we have defined a set ) analogous to 0 level of fast escaping set by using maximum...

Primary 30D05 | 37F10 | Maximum term | fast escaping sets | spider’s web | transcendental entire functions | spider's web | MATHEMATICS

Primary 30D05 | 37F10 | Maximum term | fast escaping sets | spider’s web | transcendental entire functions | spider's web | MATHEMATICS

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 8/2017, Volume 286, Issue 3, pp. 783 - 800

Hyperbolicity plays an important role in the study of dynamical systems, and is a key concept in the iteration of rational functions of one complex variable....

30D20 | Secondary 30D05 | Mathematics, general | Primary 37F10 | Mathematics | 30D15 | 37F15

30D20 | Secondary 30D05 | Mathematics, general | Primary 37F10 | Mathematics | 30D15 | 37F15

Journal Article

Constructive Approximation, ISSN 0176-4276, 12/2017, Volume 46, Issue 3, pp. 435 - 458

A classical result in the theory of Loewner’s parametric representation states that the semigroup $${{\mathfrak {U}}}_0$$ U 0 of all conformal self-maps...

Loewner–Kufarev equation | 30C75 | Parametric representation | Infinitesimal generator | Mathematics | Univalent function | Evolution family | 37C25 | 34K35 | Lie semigroup | Primary 30C35 | Loewner equation | Secondary 30D05 | Conformal mapping | Numerical Analysis | Analysis | Boundary fixed point | 30C80 | 22E99 | SINGULARITIES | UNIT DISK | ANALYTIC-FUNCTIONS | Loewner-Kufarev equation | MATHEMATICS | SEMIGROUPS | DISTORTION | MAPS | FAMILIES | KOENIGS FUNCTION | Control systems | Mathematics - Complex Variables

Loewner–Kufarev equation | 30C75 | Parametric representation | Infinitesimal generator | Mathematics | Univalent function | Evolution family | 37C25 | 34K35 | Lie semigroup | Primary 30C35 | Loewner equation | Secondary 30D05 | Conformal mapping | Numerical Analysis | Analysis | Boundary fixed point | 30C80 | 22E99 | SINGULARITIES | UNIT DISK | ANALYTIC-FUNCTIONS | Loewner-Kufarev equation | MATHEMATICS | SEMIGROUPS | DISTORTION | MAPS | FAMILIES | KOENIGS FUNCTION | Control systems | Mathematics - Complex Variables

Journal Article

Bulletin of the London Mathematical Society, ISSN 0024-6093, 02/2019, Volume 51, Issue 1, pp. 120 - 128

In complex dynamics, the bungee set is defined as the set points whose orbit is neither bounded nor tends to infinity. In this paper we study, for the first...

30C65 | 30D05 (secondary) | 37F10 (primary) | MATHEMATICS | ITERATION | FAST ESCAPING SET | POINTS

30C65 | 30D05 (secondary) | 37F10 (primary) | MATHEMATICS | ITERATION | FAST ESCAPING SET | POINTS

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 4/2018, Volume 288, Issue 3, pp. 855 - 873

...) for z ∈ J ( f ). Mathematics Subject Classiﬁcation Primary 37F10; Secondary 30D05 1 Introduction and results The Julia set J ( f ) of a rational or entire function...

Secondary 30D05 | Mathematics, general | Primary 37F10 | Mathematics | MATHEMATICS | MEROMORPHIC FUNCTIONS | MAPS | POINTS | GROWTH | Mathematics - Dynamical Systems

Secondary 30D05 | Mathematics, general | Primary 37F10 | Mathematics | MATHEMATICS | MEROMORPHIC FUNCTIONS | MAPS | POINTS | GROWTH | Mathematics - Dynamical Systems

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 6/2019, Volume 292, Issue 1, pp. 343 - 359

Devaney and Krych (Ergod Theory Dyn Syst 4:35–52, 1984) showed that for the exponential family $$\lambda e^z$$ λ e z , where $$0<\lambda <1/e$$ 0 < λ < 1 / e ,...

Hair | Secondary 37F10 | 30C65 | Eremenko–Lyubich class | Primary 30D05 | Mathematics, general | Exponential map | Differentiability | Mathematics | Complex dynamics | External ray | MATHEMATICS | Eremenko-Lyubich class

Hair | Secondary 37F10 | 30C65 | Eremenko–Lyubich class | Primary 30D05 | Mathematics, general | Exponential map | Differentiability | Mathematics | Complex dynamics | External ray | MATHEMATICS | Eremenko-Lyubich class

Journal Article

Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 4/2019, Volume 198, Issue 2, pp. 411 - 441

We study the backward invariant set of one-parameter semigroups of holomorphic self-maps of the unit disc. Such a set is foliated in maximal invariant curves,...

Petals | Holomorphic models | Semigroups of holomorphic functions | Primary 37C10 | Mathematics | 37F99 | 37C25 | 30C35 | Secondary 30D05 | Backward orbits | Koenigs function | Mathematics, general | 30C80 | MATHEMATICS | MATHEMATICS, APPLIED

Petals | Holomorphic models | Semigroups of holomorphic functions | Primary 37C10 | Mathematics | 37F99 | 37C25 | 30C35 | Secondary 30D05 | Backward orbits | Koenigs function | Mathematics, general | 30C80 | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Journal of Difference Equations and Applications, ISSN 1023-6198, 09/2017, Volume 23, Issue 9, pp. 1584 - 1596

It is well known that the bounding curve of the central hyperbolic component of the Multibrot set in the parameter space of unicritical degree d polynomials is...

Blaschke product | parameter space | epicycloid | Secondary: 37F10 | Primary: 30D05 | MATHEMATICS, APPLIED | Functions (mathematics) | Polynomials | Cusps | Mathematical analysis | Epicycloids

Blaschke product | parameter space | epicycloid | Secondary: 37F10 | Primary: 30D05 | MATHEMATICS, APPLIED | Functions (mathematics) | Polynomials | Cusps | Mathematical analysis | Epicycloids

Journal Article

Qualitative Theory of Dynamical Systems, ISSN 1575-5460, 04/2015, Volume 14, Issue 1, pp. 25 - 38

Elliptic Mobius transformations of the unit disk are those for which there is a fixed point in D. It is not hard to classify which Mobius transformations are...

Secondary 37F10 | Primary 30D05 | MATHEMATICS | MATHEMATICS, APPLIED | UNIT DISK | POINTS

Secondary 37F10 | Primary 30D05 | MATHEMATICS | MATHEMATICS, APPLIED | UNIT DISK | POINTS

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 9/2019, Volume 42, Issue 5, pp. 1993 - 2008

The iteration of the map $$z \mapsto \lambda + \tan z$$ z ↦ λ + tan z on the complex plane is investigated for each complex number $$\lambda $$ λ . It is shown...

Parameter plane | Secondary 30D05 | Translated tangents | Completely invariant Fatou component | Mathematics, general | Totally disconnected Julia set | Primary 37F10 | Mathematics | Applications of Mathematics | MATHEMATICS | DYNAMICS | Invariants

Parameter plane | Secondary 30D05 | Translated tangents | Completely invariant Fatou component | Mathematics, general | Totally disconnected Julia set | Primary 37F10 | Mathematics | Applications of Mathematics | MATHEMATICS | DYNAMICS | Invariants

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 6/2018, Volume 186, Issue 2, pp. 299 - 314

We say that a finite subset E of the Euclidean plane $$\mathbb {R}^2$$ R2 has the discrete Pompeiu property with respect to isometries (similarities), if,...

39B32 | Functional equations | Discrete Pompeiu problem | Mathematics, general | Mathematics | 43A45 (secondary) | Spectral analysis | 30D05 (primary) | MATHEMATICS

39B32 | Functional equations | Discrete Pompeiu problem | Mathematics, general | Mathematics | 43A45 (secondary) | Spectral analysis | 30D05 (primary) | MATHEMATICS

Journal Article

Proceedings of the London Mathematical Society, ISSN 0024-6115, 07/2018, Volume 117, Issue 1, pp. 100 - 124

Baker's conjecture states that a transcendental entire function of order less than 1/2 has no unbounded Fatou components. It is known that, for such functions,...

30D20 | 37F10 (secondary) | 30D05 (primary) | MATHEMATICS | ITERATION | FATOU COMPONENTS | SMALL GROWTH | DOMAINS

30D20 | 37F10 (secondary) | 30D05 (primary) | MATHEMATICS | ITERATION | FATOU COMPONENTS | SMALL GROWTH | DOMAINS

Journal Article

Complex Variables and Elliptic Equations, ISSN 1747-6933, 04/2019, Volume 64, Issue 4, pp. 701 - 709

We consider semigroups generated by two rational functions whose Julia sets are Cantor targets. Noting that a Cantor target has no interior points, we...

Y. Antipov | Hausdorff dimension | cantor target | Primary 37F10 | semigroup | Complex dynamics | Julia set | Secondary 30D05 | MATHEMATICS | Mathematical analysis | Polynomials | Rational functions

Y. Antipov | Hausdorff dimension | cantor target | Primary 37F10 | semigroup | Complex dynamics | Julia set | Secondary 30D05 | MATHEMATICS | Mathematical analysis | Polynomials | Rational functions

Journal Article

Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 2/2015, Volume 194, Issue 1, pp. 221 - 245

We characterize regular fixed points of evolution families in terms of analytical properties of the associated Herglotz vector fields and geometrical...

Loewner chain | Primary 37C10 | Mathematics | Evolution family | Univalent function | 37F99 | 37C25 | 30C35 | Secondary 30D05 | Conformal mapping | Boundary fixed point | Mathematics, general | 30C80 | MATHEMATICS, APPLIED | BEHAVIOR | EVOLUTION FAMILIES | ANALYTIC-FUNCTIONS | MATHEMATICS | SEMIGROUPS | CHAINS | KOENIGS FUNCTION | Family | Analysis

Loewner chain | Primary 37C10 | Mathematics | Evolution family | Univalent function | 37F99 | 37C25 | 30C35 | Secondary 30D05 | Conformal mapping | Boundary fixed point | Mathematics, general | 30C80 | MATHEMATICS, APPLIED | BEHAVIOR | EVOLUTION FAMILIES | ANALYTIC-FUNCTIONS | MATHEMATICS | SEMIGROUPS | CHAINS | KOENIGS FUNCTION | Family | Analysis

Journal Article

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