zbMath1196.14002arXivmath/0407433MaRDI QIDQ5306021
Robert S. Rumely, Matthew H. Baker
Publication date: 24 March 2010
Full work available at URL: https://arxiv.org/abs/math/0407433
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Skeletons and tropicalizations,
On a characterization of polynomials among rational functions in non-Archimedean dynamics,
Parabolic bifurcation loci in the spaces of rational functions,
Uniform perfectness of the Berkovich Julia sets in non-archimedean dynamics,
Non-Archimedean indifferent components of rational functions that are not disks,
Equidistribution of small points, rational dynamics, and potential theory,
Degenerations of complex dynamical systems. II: Analytic and algebraic stability,
A non-Archimedean Ohsawa-Takegoshi extension theorem,
The critical height is a moduli height,
Energy minimization principle for non-Archimedean curves,
Dynamics of commuting rational maps on Berkovich projective space over \(\mathbb C_p\),
Infinitesimal deformation of \(p\)-adic differential equations on Berkovich curves,
Equidistribution of the crucial measures in non-Archimedean dynamics,
Berkovich curves and Schottky uniformization. I: The Berkovich affine line,
Berkovich curves and Schottky uniformization. II: Analytic uniformization of Mumford curves,
Faithful tropicalizations of elliptic curves using minimal models and inflection points,
Energy integrals and small points for the Arakelov height,
Topology and geometry of the Berkovich ramification locus for rational functions. I,
Radius of convergence of \(p\)-adic connections and the \(p\)-adic Rolle theorem,
A Riemann-Hurwitz formula for skeleta in non-Archimedean geometry,
Hyperbolicity notions for varieties defined over a non-Archimedean field,
A dynamical construction of small totally \(p\)-adic algebraic numbers,
Variation of canonical height for Fatou points on \(\mathbb{P}^1\),
An a priori bound for rational functions on the Berkovich projective line,
Apéry base and polar invariants for real valuations,
Fekete configuration, quantitative equidistribution and wandering critical orbits in non-archimedean dynamics,
Boundedness of hyperbolic components of Newton maps,
Valuations and asymptotic invariants for sequences of ideals,
Preperiodic points and unlikely intersections,
Dynamics of transcendental entire maps on Berkovich affine line,
Rational maps with rational multipliers,
Non-archimedean connected Julia sets with branching,
On minimal decomposition of \(p\)-adic homographic dynamical systems,
Rescaling limits in non-Archimedean dynamics,
A Mahler-type estimate of weighted Fekete sums on the Berkovich projective line,
Attracting cycles in \(p\)-adic dynamics and height bounds for postcritically finite maps,
Puiseux series dynamics of quadratic rational maps,
Real valuations on skew polynomial rings,
The pointwise convergence of \(p\)-adic Möbius maps,
Retracted article: Radius of convergence of \(p\)-adic connections and the Berkovich ramification locus,
On the heights of totally \(p\)-adic numbers,
Computing conjugating sets and automorphism groups of rational functions,
Lower bounds for non-Archimedean Lyapunov exponents,
Approximation of non-archimedean Lyapunov exponents and applications over global fields,
The convergence Newton polygon of a \(p\)-adic differential equation. I: Affinoid domains of the Berkovich affine line,
The convergence Newton polygon of a \(p\)-adic differential equation. II: Continuity and finiteness on Berkovich curves,
The valuative capacity of subshifts of finite type,
Canonical measures on metric graphs and a Kazhdan's theorem,
Metric estimates and membership complexity for Archimedean amoebae and tropical hypersurfaces,
Poincaré duality for the tropical Dolbeault cohomology of non-Archimedean Mumford curves,
Height bounds for algebraic numbers satisfying splitting conditions,
Minimality of \(p\)-adic rational maps with good reduction,
Faithful tropicalization of Mumford curves of genus two,
Value distribution of derivatives in polynomial dynamics,
Rational map \(ax + 1/x\) on the projective line over \(\mathbb{Q}_2\),
Tropical dynamics of area-preserving maps,
Positivity properties of metrics and delta-forms,
Preperiodic points for families of rational maps,
Nonmaximal ideals and the Berkovich space of the algebra of bounded analytic functions,
Some problems of arithmetic origin in rational dynamics,
Comparison of two notions of subharmonicity on non-archimedean curves,
Degenerations of \(\mathrm{SL}(2, \mathbb{C})\) representations and Lyapunov exponents,
On measure-preserving $\mathcal {C}^1$ transformations of compact-open subsets of non-archimedean local fields,
Singular semipositive metrics in non-Archimedean geometry,
Rational map 𝑎𝑥+1/𝑥 on the projective line over ℚ_{𝕡},
A criterion for weak convergence on Berkovich projective space,
Good formal structures for flat meromorphic connections. I: Surfaces,
Degenerating families of dendrograms,
Quantitative approximations of the Lyapunov exponent of a rational function over valued fields,
Dynamical uniform boundedness and the \(abc\)-conjecture,
Configuration of the crucial set for a quadratic rational map,
Limits of rational maps, \(\mathbb{R}\)-trees and barycentric extension,
Geometric formulas on Rumely's weight function and crucial measure in non-archimedean dynamics,
Order of torsion for reduction of linearly independent points for a family of Drinfeld modules,
Quantitative logarithmic equidistribution of the crucial measures,
Forms and Currents on the Analytification of an Algebraic Variety (After Chambert-Loir and Ducros),
The Non-Archimedean Monge–Ampère Equation,
Convergence Polygons for Connections on Nonarchimedean Curves,
Analytification and Tropicalization Over Non-archimedean Fields,
Degeneration of Linear Series from the Tropical Point of View and Applications,
J-stability in non-Archimedean dynamics,
Equidistribution in non-Archimedean parameter curves towards the activity measures,
Radiality of definable sets,
Common preperiodic points for quadratic polynomials,
Metric graphs, cross ratios, and Rayleigh's laws,
Trees, length spectra for rational maps via barycentric extensions, and Berkovich spaces,
Tropical varieties for exponential sums,
The valuative tree is the projective limit of Eggers-Wall trees,
-stability of expanding maps in non-Archimedean dynamics,
Nonarchimedean geometry of Witt vectors,
The Arakelov-Zhang pairing and Julia sets,
Wandering Fatou Components and Algebraic Julia Sets,
On metric properties of limit sets of contractive analytic non-Archimedean dynamical systems,
Non-Archimedean Koksma inequalities, variation, and Fourier analysis,
Lifting harmonic morphisms. I: Metrized complexes and Berkovich skeleta,
Berkovich spaces embed in Euclidean spaces,
Rescaling limits of complex rational maps,
Reified valuations and adic spectra,
Non-Archimedean normal families,
DEGENERATIONS OF COMPLEX DYNAMICAL SYSTEMS,
Bounded hyperbolic components of bicritical rational maps,
Oscillating wandering domains for p$p$‐adic transcendental entire maps,
Points de petite hauteur sur une variété semi‐abélienne de la forme Gmn×A$\mathbb {G}_m^n \times A$,
Indeterminacy loci of iterate maps in moduli space,
Homoclinic orbits, multiplier spectrum and rigidity theorems in complex dynamics,
Spectrum of \(p\)-adic linear differential equations. I: The shape of the spectrum,
Self‐adjoint and Markovian extensions of infinite quantum graphs,
Tropical moments of tropical Jacobians,
Quasi-adelic measures and equidistribution on,
Global pluripotential theory over a trivially valued field,
Berkovich dynamics of Newton maps,
Uniformizer of the false Tate curve extension of ℚp (II),
Collision of orbits for a one-parameter family of Drinfeld modules,
A dynamical pairing between two rational maps,
Faithful tropicalisation and torus actions,
Rationality of dynamical canonical height,
Quantitative height bounds under splitting conditions,
Current trends and open problems in arithmetic dynamics,
On Fibonacci polynomials and wandering domains: Figure 1.,
Solution to a non-Archimedean Monge-Ampère equation,
Finite morphisms between projective varieties and Skeleta,
Canonical Heights and Preperiodic Points for Certain Weighted Homogeneous Families of Polynomials,
The minimal resultant locus,
Equidistribution and the heights of totally real and totally p-adic numbers,
Bifurcation measures and quadratic rational maps