Alan Frank Beardon

Alan Frank Beardon's AcademicInfluence.com Rankings

Alan Frank Beardon

Mathematics

#3572

World Rank

#5248

Historical Rank

Measure Theory

#1559

World Rank

#1935

Historical Rank

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Mathematics

Why Is Alan Frank Beardon Influential?

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According to Wikipedia, Alan Frank Beardon is a British mathematician. Education and career Beardon obtained his doctorate at Imperial College London in 1964, supervised by Walter Hayman. In 1970 he was appointed as a lecturer in the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge, with promotions to readership and professorship until his retirement in 2007. He is an emeritus fellow of St. Catherine's College, Cambridge.

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Alan Frank Beardon's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

The Geometry of Discrete Groups (1995) (975)
Iteration of Rational Functions (1991) (818)
The hyperbolic metric and geometric function theory (2006) (201)
Limit points of Kleinian groups and finite sided fundamental polyhedra (1974) (199)
Iteration of Rational Functions: Complex Analytic Dynamical Systems (1991) (198)
The Poincaré Metric of Plane Domains (1978) (167)
Sums of Powers of Integers (1996) (110)
Pommerenke, The Poincare metric of plane domains (1978) (109)
Symmetries of julia sets (1990) (85)
A primer on Riemann surfaces (1984) (80)
The Apollonian Metric of a Domain in ℝ n (1998) (75)
The non-existence of a utility function and the structure of non-representable preference relations (2002) (69)
Algebra and Geometry (2005) (65)
THE HAUSDORFF DIMENSION OF SINGULAR SETS OF PROPERLY DISCONTINUOUS GROUPS. (1966) (55)
Inequalities for certain Fuchsian groups (1971) (52)
The dynamics of contractions (1997) (48)
The Schwarz-Pick Lemma for circle packings (1991) (43)
On the Hausdorff dimension of general Cantor sets (1965) (42)
The Exponent of Convergence of Poincaré Series (1968) (41)
Iteration of Contractions and Analytic Maps (1990) (39)
Schwarzian derivatives, the Poincaré metric and the kernel function (1980) (39)
On the convergence of Padé approximants (1968) (35)
Sphere-preserving maps in inversive geometry (2001) (34)
Complex analysis: The argument principle in analysis and topology (1979) (33)
The zeros of linear combinations of orthogonal polynomials (2005) (30)
Smale's Mean Value conjecture and the hyperbolic metric (2002) (30)
The Theorems of Stieltjes and Favard (2011) (30)
Closed geodesics on a Riemann surface with application to the Markov spectrum (1986) (29)
Fibonacci, Chebyshev, and Orthogonal Polynomials (2005) (28)
Pell's Equation and Two Generator Free Möbius Groups (1993) (27)
Spiral hexagonal circle packings in the plane (1994) (26)
DIFFERENTIAL GEOMETRY AND COMPLEX ANALYSIS H. E. RAUCH MEMORIAL VOLUME (1986) (26)
Poiynomials with identical Julia sets (1992) (24)
Geodesic continued fractions (2012) (23)
Barycentric subdivision of triangles and semigroups of Mobius maps (1996) (23)
The Metric Dimension of Metric Spaces (2013) (23)
A multi-point Schwarz-Pick Lemma (2004) (22)
THE UTILITY THEOREMS OF WOLD, DEBREU, AND ARROW-HAHN (1994) (22)
On Ritt's Factorization of Polynomials (2000) (21)
On the k-metric dimension of metric spaces (2016) (21)
Debreu's Gap Theorem (1992) (21)
Random iteration of analytic maps (2004) (21)
Lexicographic decomposition of chains and the concept of a planar chain (2002) (20)
The Klein, Hilbert and Poincaré metrics of a domain (1999) (19)
The Schwarz-Pick Lemma for derivatives (1997) (18)
The components of a Julia set (1991) (17)
Diophantine triples (2002) (16)
The Seidel, Stern, Stolz and Van Vleck Theorems on continued fractions (2010) (16)
Normal Families: a Geometric Perspective (2014) (15)
Integral means of subharmonic functions (1971) (15)
A strengthening of the Schwarz-Pick inequality (1992) (15)
Continued Fractions and Restrained Sequences of Mobius Maps (2004) (14)
The Geometry of Pringsheim's Continued Fractions (2001) (14)
Circle packings in different geometries (1991) (14)
Entire Solutions of f(kz) = kf(z)f′(z) (2012) (13)
Parameterizations of algebraic curves. (2006) (13)
Worpitzky's Theorem on continued fractions (2001) (12)
Limits: A New Approach to Real Analysis (1997) (11)
Utility functions and the order type of the continuum (1994) (10)
On Classical Series Associated with Kleinian Groups (1972) (10)
Resolving the hypercube (2013) (10)
Periodic orbits of difference equations (1995) (10)
A Geometric Representation of Continued Fractions (2014) (9)
On the location of poles of Padé approximants (1968) (9)
The hyperbolic metric in a rectangle. II. (2003) (9)
THE HYPERBOLIC METRIC OF A RECTANGLE (2001) (8)
Montel's theorem for subharmonic functions and solutions of partial differential equations (1971) (8)
Curvature, circles, and conformal maps (1986) (8)
The Principal Branch of the Lambert W Function (2020) (8)
Utility theory and continuous monotonic functions (1994) (8)
Repeated Compositions of Analytic Maps (2001) (8)
Magic labellings of infinite graphs (2004) (8)
PARAMETRIZATIONS OF ALGEBRAIC CURVES (2006) (8)
Hyperbolic Polygons and Fuchsian Groups (1979) (7)
The Pointwise convergence of Möbius maps (2004) (7)
On the Pointwise Limit of Complex Analytic Functions (2003) (7)
DISCRETE GROUPS IN SPACE AND UNIFORMIZATION PROBLEMS (1994) (7)
The Uniformisation of a Twice-Punctured Disc (2012) (7)
Continued Fractions, Möbius Transformations and Clifford Algebras (2003) (7)
Totally ordered subsets of Euclidean space (1994) (6)
THE GENERALIZED CAPACITY OF CANTOR SETS (1968) (6)
Euclidean and hyperbolic lengths of images of arcs (2007) (6)
Fuchsian groups and nth roots of parabolic generators (1988) (6)
The Hillam–Thron Theorem in Higher Dimensions (2003) (6)
Fundamental domains for finitely generated Kleinian groups. (1975) (6)
Ford and Dirichlet Regions for Fuchsian Groups (1982) (6)
The geometry of Riemann surfaces (2001) (6)
Efficient sets are small (2013) (6)
Iteration of Analytic Euclidean Contractions (1995) (6)
Stable Sets in Multi-Good Pillage Games are Small (2010) (6)
On the Isometric Circles of Elements in a Fuchsian Group (1975) (6)
The norm of a Möbius transformation (1984) (5)
Composition factors of polynomials (2001) (5)
FUNDAMENTAL DOMAINS FOR KLEINIAN GROUPS (1974) (5)
Sums of squares of digits (1998) (5)
Dieudonné Points of Holomorphic Self-Maps of Regions (2008) (5)
The Worpitzky-Pringsheim Theorem on Continued Fractions (2001) (4)
Zeros of polynomials embedded in an orthogonal sequence (2011) (4)
Norms of Möbius maps (2010) (4)
91.30 Fibonacci meets Chebyshev (2007) (4)
Semi-Groups of Analytic Maps (2001) (4)
A remark on the shape of quadratic Julia sets (1994) (4)
The Differentiation of a Composite Function (1971) (4)
Contractions of the Real Line (2006) (4)
The Real Solutions of x y = y x (1966) (4)
The maximum degree in a vertex-magic graph (2004) (4)
Conformal Images and the Angle of Parallelism (2012) (4)
Transcendental Dynamics and Complex Analysis: Conformal automorphisms of finitely connected regions (2008) (3)
The Hausdorff dimension of singular sets of properly discontinuous groups in $N$-dimensional space (1965) (3)
SOME REMARKS ON NON-DISCRETE MÖBIUS GROUPS (2008) (3)
The Heron parameters of a triangle (2015) (3)
The Diameter of a Hyperbolic Disc (2011) (3)
Even and odd entire functions (2003) (3)
Van Vleck’s Theorem on Continued Fractions (2007) (3)
Convex fundamental domains of Fuchsian groups (1974) (3)
Utility representation of continuous preferences (1997) (3)
S•P numbers (1999) (2)
Strongly Discrete Subgroups of SL(2,C) (1981) (2)
An Extension of Montel’s Three Omitted Values Theorem (2021) (2)
Frieze groups, cylinders, and quotient groups (2013) (2)
Finite groups, wallpaper patterns and non-euclidean geometries (1978) (2)
The convexity of the function y = E(x) defined by xy = yx (2020) (2)
Circles, chords and epicycloids (1989) (2)
The metric dimension (2016) (2)
Approximants of Sleszynski-Pringsheim continued fractions (2001) (2)
Quasi-indifference classes in utility theory (1995) (2)
The Structure of Words in Discrete Subgroups of Sl(2, C) (1975) (2)
Cyclic Absolute Differences of Integers (2011) (1)
Real and Complex Numbers (1997) (1)
Kleinian groups with unbounded limit sets (1972) (1)
III.79 Riemann Surfaces (2010) (1)
Lengths and angles (2016) (1)
Topology and Preference Relations (2020) (1)
Conformal Symmetries of Regions (2007) (1)
A remark on analytic continuation (1999) (1)
THE APOLLONIAN METRIC AND BILIPSCHITZ MAPPINGS (2003) (1)
Two examples of Julia sets (1992) (1)
The Uniformisation of the Equation $$z^w=w^z$$ z w = w (2021) (1)
The average degree in a vertex-magic graph (2006) (1)
101.03 Products of 3 × 3 magic matrices (2017) (1)
Automorphic forms on nondiscrete Möbius groups (1996) (1)
Creative Mathematics: A Gateway to Research (2009) (1)
What is the most symmetric quadrilateral? (2012) (1)
Complex Möbius Transformations (1983) (1)
On the Continuity of Monotonic Functions (1967) (1)
The Divergence of Two Hyperbolic Geodesics (2012) (1)
Prime matrices and prime polynomials (2009) (1)
The vector triple product (2002) (1)
A disc rolling in a tray (2002) (1)
Lie products, closed geodesics and Fuchsian groups (1982) (1)
Paying for parking (2016) (0)
Winding Numbers, Unwinding Numbers, and the Lambert W Function (2021) (0)
Algebra and Geometry: Vector spaces (2005) (0)
Surjective isometries of metric geometries (2020) (0)
Winding Numbers, Unwinding Numbers, and the Lambert W Function (2021) (0)
Normal Families of Möbius Maps (2020) (0)
105.26 Areas above and below a curve (2021) (0)
Printed in the United Kingdom Random iteration of analytic maps (2004) (0)
Summary. Debreu's fundamental result on the existence of utility functions that are continuous with respect to the order topology requires his Gap Theorem. A (1992) (0)
Index to the Mathematical Gazette (2011) (0)
Algebra and Geometry: Groups (2005) (0)
Algebra and Geometry: Groups and permutations (2005) (0)
87.08 The dimension of the space of magic squares (2003) (0)
University ’ s repository of research publications and other research outputs The Seidel , Stern , Stolz and Van Vleck Theorems on continued fractions Journal Item (2018) (0)
Addendum to our paper “The Schwarz-Pick lemma for circle packings” (1992) (0)
Normal Families: a Geometric Perspective (2014) (0)
Index to the Mathematical Gazette (1979) (0)
79.55 A simple inequality (1995) (0)
Extensions of the Modular Group (2016) (0)
Properties of the Julia Set (1991) (0)
Extensions of the Modular Group (2015) (0)
Population dynamics with chaos and extinction (2011) (0)
Geoboards, polygons and Pick’s Theorem (2009) (0)
Non-discrete Frieze Groups (2016) (0)
Cortona Summer Course Notes (2003) (0)
91.36 Functional equations and groups (2007) (0)
106.33 Fibonacci numbers and Cassini’s identity (2022) (0)
Removing a vertex from a tetrahedron (2015) (0)
Primes and irreducible elements (2016) (0)
Population dynamics with chaos and extinction (2013) (0)
LINEAR DIFFERENTIAL EQUATIONS AND GROUP THEORY FROM RIEMANN TO POINCARÉ (1988) (0)
The real solutions of x = ax (2022) (0)
Feedback (2016) (0)
Elementary Problems: E1875-E1884 (1966) (0)
Who wants to be a manager. (1980) (0)
Geometric Group Theory: Group Actions and Riemann Surfaces (1993) (0)
89.17 Flexible quadrilaterals (2005) (0)
Fatou and Julia sets (2019) (0)
On the Behavior of a Special Series (1968) (0)
University of Birmingham Efficient sets are small (2013) (0)
96.04 Pythagorean equations (2012) (0)
Algebra and Geometry: Matrices (2005) (0)
The symmetries of a quadrilateral (2016) (0)
104.24 Surveying in the hyperbolic plane (2020) (0)
Algebra and Geometry: The real numbers (2005) (0)
Groups of Rotations of Euclidean and Hyperbolic Spaces (2022) (0)
Introduction to complex analysis (1984) (0)
Conformal Automorphisms of Plane Domains (1985) (0)
Meromorphic Self-Maps of Regions (2011) (0)
102.05 Remarks on Problem 100.I (2018) (0)
101.34 The area of a quadrilateral (2017) (0)
Diameter of maximally symmetric compact Riemann surfaces (2023) (0)
Algebra and Geometry: Linear equations (2005) (0)
Algebra and Geometry: Eigenvectors (2005) (0)
Index to the Mathematical Gazette (1978) (0)
Universal Constraints On Fuchsian Groups (1983) (0)
96.35 Reflections on lattices (2012) (0)
The No Wandering Domains Theorem (1991) (0)
Algebra and Geometry: Spherical geometry (2005) (0)
Length inequalities for Riemann surfaces (2013) (0)
Whose job is staff care? (1978) (0)
Circumscribed hyperbolic triangles (2022) (0)
Pitot's theorem, dynamic geometry and conics (2021) (0)
Fuchsian groups , by Svetlana Katok. Pp. 175. £11.95, 1992 ISBN 0-226-42583-5 (University of Chicago Press) (1993) (0)
The Structure of the Fatou Set (1991) (0)
Multiply Connected Domains Which Are Conformally Equivalent To Certain Symmetrical Domains (1965) (0)
On 105.28 (2022) (0)
Repeated vector products (2020) (0)
Double Cosets, Rotations and Isometric Circles (2021) (0)
Complex Analytic Functions (2016) (0)
Index to the Mathematical Gazette (2002) (0)
Algebra and Geometry: Möbius transformations (2005) (0)
An Extension of Montel’s Three Omitted Values Theorem (2021) (0)
Sums of powers of digits (2016) (0)
Möbius Maps and Periodic Continued Fractions (2015) (0)
Feedback (2015) (0)
Algebra and Geometry: Quaternions and isometries (2005) (0)
Canonical generators of Fuchsian groups (1981) (0)
π, γ, e, and n! (1997) (0)
Mathematical Explorations by Alan F. Beardon (2016) (0)
Forward Invariant Components (1991) (0)
Geometric Julia–Wolff Theorems for Weak Contractions (2022) (0)
84.40 Reflections on Euclid’s algorithm (2000) (0)
Review (2012) (0)
Removing a vertex (2016) (0)
Complex Exponents and Group Theory (2020) (0)
Squares within squares (2016) (0)
Algebra and Geometry: Vectors in three-dimensional space (2005) (0)
Algebra and Geometry: Linear maps of Euclidean space (2005) (0)
The Metric Dimension of Metric Spaces (2013) (0)
Finitely Generated Groups (1983) (0)
Algebra and Geometry: The complex plane (2005) (0)
99.36 Stable tables (2015) (0)
The Equation f(2x) = 2f(x)f′(x) (2013) (0)
Möbius Transformations on ℝ n (1983) (0)
The three Steiner-Lehmus theorems (2019) (0)
SOME REMARKS ON NON-DISCRETE M ¨ (1996) (0)
Fundamental Domains and Cyclic Subgroups of Fuchsian Groups (1980) (0)
In the Pipeline for July 2023 (2023) (0)
Polynomials of Magic Matrices (2019) (0)
How to use this book (2016) (0)
A rolling disc (2016) (0)
On 106.17 (2022) (0)
80.6 Square roots of involutions (1996) (0)
Algebra and Geometry: Group actions (2005) (0)
Sets and Functions (1997) (0)
In the pipeline for March 2020 (2019) (0)
95.20 Integral inequalities in probability theory (2011) (0)
Diameter of Compact Riemann Surfaces (2023) (0)
102.54 Unravelling Simpson's paradox (2018) (0)
On the Hausdorff dimension of certain sets (1964) (0)

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