The dynamics of Pythagorean Triples

DOI10.1090/S0002-9947-08-04467-XzbMath1161.37012arXivmath/0406512OpenAlexW1965908864WikidataQ56059562 ScholiaQ56059562MaRDI QIDQ3532555

Dan Romik

Publication date: 28 October 2008

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0406512

zbMATH Keywords

ternary expansionprimitive pythagorean triple

Mathematics Subject Classification ID

Related Items (16)

Number theoretical properties of Romik's dynamical system ⋮ On similarity classes of well-rounded sublattices of \(\mathbb Z^2\) ⋮ Odd-odd continued fraction algorithm ⋮ Attractors of dual continued fractions ⋮ Unnamed Item ⋮ The Apollonian structure of Bianchi groups ⋮ On Minkowski type question mark functions associated with even or odd continued fractions ⋮ Billiards on Pythagorean triples and their Minkowski functions ⋮ Intrinsic Diophantine approximation on the unit circle and its Lagrange spectrum ⋮ Slow continued fractions, transducers, and the Serret theorem ⋮ Quadratic forms and their Berggren trees ⋮ Finite Gauss transformations ⋮ A Forest of Eisensteinian Triangles ⋮ The dynamics of Super-Apollonian continued fractions ⋮ Lagrange spectrum of a circle over the Eisensteinian field ⋮ Non-freeness of groups generated by two parabolic elements with small rational parameters

Uses Software

• OEIS

Cites Work

• Recursive generation of primitive Pythagorean triples
• Dynamical analysis of a class of Euclidean algorithms.
• Euclidean algorithms are Gaussian
• Height and Excess of Pythagorean Triples
• The Modular Surface and Continued Fractions
• Cross section map for the geodesic flow on the modular surface
• The Modular Tree of Pythagoras
• The backward continued fraction map and geodesic flow
• A Genealogy of 120^⚬ and 60^⚬ Natural Triangles
• The Poincaré series of $\mathbb C\setminus\mathbb Z$
• Patterns of Visible and Nonvisible Lattice Points
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The dynamics of Pythagorean Triples