Results 11 to 20 of about 1,594 (52)
Diophantine non-integrability of a third order recurrence with the Laurent property [PDF]
, 2006 We consider a one-parameter family of third order nonlinear recurrence relations. Each member of this family satisfies the singularity confinement test, has a conserved quantity, and moreover has the Laurent property: all of the iterates are Laurent ...
Hone, Andrew N.W.
core +2 more sources
Heights and quadratic forms: on Cassels' theorem and its generalizations [PDF]
, 2012 In this survey paper, we discuss the classical Cassels' theorem on existence of small-height zeros of quadratic forms over Q and its many extensions, to different fields and rings, as well as to more general situations, such as existence of totally ...
Fukshansky, Lenny
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A Kolmogorov theorem for nearly-integrable Poisson systems with asymptotically decaying time-dependent perturbation [PDF]
, 2014 The aim of this paper is to prove the Kolmogorov theorem of persistence of Diophantine flows for nearly-integrable Poisson systems associated to a real analytic Hamiltonian with aperiodic time dependence, provided that the perturbation is asymptotically ...
A Fortunati +11 more
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On the algebraic structure of rational discrete dynamical systems [PDF]
, 2015 We show how singularities shape the evolution of rational discrete dynamical systems. The stabilisation of the form of the iterates suggests a description providing among other things generalised Hirota form, exact evaluation of the algebraic entropy as ...
Viallet, Claude M.
core +3 more sources
Laurent Polynomials and Superintegrable Maps [PDF]
, 2007 This article is dedicated to the memory of Vadim Kuznetsov, and begins with some of the author's recollections of him. Thereafter, a brief review of Somos sequences is provided, with particular focus being made on the integrable structure of Somos-4 ...
Hone, Andrew N.W.
core +1 more source
Integral Points for Multi-norm Tori
, 2012 We construct a finite subgroup of Brauer-Manin obstruction for detecting the existence of integral points on integral models of principle homogeneous spaces of multi-norm tori. Several explicit examples are provided.Comment: 25 pages.
Wei, Dasheng, Xu, Fei
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p-adic Numbers and the Hasse Principle [PDF]
, 2014 Hasse’s local-global principle is the idea that one can find an integer solution to anequation by using the Chinese remainder theorem to piece together solutions modulo powers of each different prime number.
Benjakob, Otmar
core
Explicit Chabauty-Kim theory for the thrice punctured line in depth two
, 2014 Let $X= \mathbb{P}^1 \setminus \{0,1,\infty\}$, and let $S$ denote a finite set of prime numbers. In an article of 2005, Minhyong Kim gave a new proof of Siegel's theorem for $X$: the set $X(\mathbb{Z}[S^{-1}])$ of $S$-integral points of $X$ is finite ...
Beı˘linson +26 more
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Elliptic Curves and Hyperdeterminants in Quantum Gravity [PDF]
, 2010 Hyperdeterminants are generalizations of determinants from matrices to multi-dimensional hypermatrices. They were discovered in the 19th century by Arthur Cayley but were largely ignored over a period of 100 years before once again being recognised as ...
Gibbs, Philip
core
Weyl's inequality and systems of forms
, 2014 By providing a variant of Weyl's inequality for general systems of forms we establish the Hardy-Littlewood asymptotic formula for the density of integer zeros of systems of quadratic or cubics forms under weaker rank conditions than previously known.
Dietmann, Rainer
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