DOI10.1007/978-3-319-00888-2zbMath1276.00006OpenAlexW2498676440WikidataQ55969513 ScholiaQ55969513MaRDI QIDQ2840319
Martin Aigner
Publication date: 18 July 2013
Full work available at URL: https://doi.org/10.1007/978-3-319-00888-2
The hyperbolic geometry of Markov's theorem on Diophantine approximation and quadratic forms ⋮
Diophantine equations via cluster transformations ⋮
The $q$-analog of the Markoff injectivity conjecture over the language of a balanced sequence ⋮
Note on character varieties and cluster algebras ⋮
Boundary slopes for the Markov ordering on relatively prime pairs ⋮
Unnamed Item ⋮
On Hermite’s problem, Jacobi–Perron type algorithms, and Dirichlet groups ⋮
Generalized Markoff equations and Chebyshev polynomials ⋮
Generalised Markov numbers ⋮
Farey boat: continued fractions and triangulations, modular group and polygon dissections ⋮
Intrinsic Diophantine approximation on the unit circle and its Lagrange spectrum ⋮
Cycle integrals of modular functions, Markov geodesics and a conjecture of Kaneko ⋮
Composition laws on the Fricke surface and Markov triples ⋮
Markov spectra for modular billiards ⋮
Continued fractions and orderings on the Markov numbers ⋮
Reprint of: ``Palindromization and construction of Markoff triples ⋮ Cluster duality between Calkin-Wilf tree and Stern-Brocot tree ⋮ A \(q\)-analog of the Markoff injectivity conjecture holds ⋮ Arithmetic and dynamics on varieties of Markoff type ⋮ Conway's light on the shadow of Mordell ⋮ The Markoff theory and the commutator subgroup \( \mathrm{SL} (2, \mathbb Z)'\) ⋮ Intrinsic Diophantine approximation on circles and spheres ⋮ Lyapunov spectrum of Markov and Euclid trees ⋮ Shadow sequences of integers: from Fibonacci to Markov and back ⋮ On the Stern-Brocot expansion of real numbers ⋮ Cluster algebras and continued fractions ⋮ Generalization of Markov Diophantine equation via generalized cluster algebra ⋮ A hyperbolic analogue of the Rademacher symbol ⋮ Non-planarity of Markoff graphs \(\mod p\) ⋮ Exceptional collections in surface-like categories ⋮ Combinatorial aspects of exceptional sequences on (rational) surfaces ⋮ On $k$-abelian equivalence and generalized Lagrange spectra ⋮ Farey recursive functions ⋮ Golden ratio and phyllotaxis, a clear mathematical link ⋮ A gap of the exponents of repetitions of Sturmian words ⋮ The Markoff equation over polynomial rings ⋮ Snake graphs and 70 ⋮ The sum of Lagrange numbers ⋮ Markov numbers and Lagrangian cell complexes in the complex projective plane ⋮ Markoff triples and strong approximation ⋮ A Correspondence between Rigid Modules Over Path Algebras and Simple Curves on Riemann Surfaces ⋮ The $*$-Markov equation for Laurent polynomials ⋮ Markov numbers, Mather’s β function and stable norm ⋮ On model-theoretic connected components in some group extensions ⋮ Christoffel words and weak Markoff theory ⋮ Unnamed Item ⋮ On quadratic numbers and forms, and Markoff theory ⋮ Palindromization and construction of Markoff triples ⋮ Palindromic sequences of the Markov spectrum ⋮ A continuity of cycle integrals of modular functions ⋮ On the Markov numbers: fixed numerator, denominator, and sum conjectures ⋮ Bowditch’s Q-conditions and Minsky’s primitive stability ⋮ Conway topograph, -dynamics and two-valued groups ⋮ A bridge between Conway–Coxeter friezes and rational tangles through the Kauffman bracket polynomials ⋮ On the Lévy constants of Sturmian continued fractions ⋮ Automorphisms of surfaces of Markov type ⋮ Lagrange spectrum of a circle over the Eisensteinian field ⋮ Partitions of unity in \(\mathrm{SL}(2,\mathbb Z)\), negative continued fractions, and dissections of polygons ⋮ Kesten-McKay law for the Markoff surface mod \(p\) ⋮ An asymptotic formula for integer points on Markoff-Hurwitz varieties ⋮ Markov and Lagrange spectra for Laurent series in $1/T$ with rational coefficients ⋮ On the ordering of the Markov numbers ⋮ Experiments with the Markoff Surface ⋮ Studies on finite Sturmian words
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