Zobrazeno 1 - 10
of 199
pro vyhledávání: '"Hone, A. N. W."'
Autor:
Harrow, J. W. E., Hone, A. N. W.
Motivated by the search for an appropriate notion of a cluster superalgebra, incorporating Grassmann variables, Ovsienko and Tabachnikov considered the extension of various recurrence relations with the Laurent phenomenon to the ring of dual numbers.
Externí odkaz:
http://arxiv.org/abs/2409.00406
We consider discrete dynamical systems obtained as deformations of mutations in cluster algebras associated with finite-dimensional simple Lie algebras. The original (undeformed) dynamical systems provide the simplest examples of Zamolodchikov period
Externí odkaz:
http://arxiv.org/abs/2403.00721
We extend recent work of the third author and Kouloukas by constructing deformations of integrable cluster maps corresponding to the Dynkin types $A_{2N}$, lifting these to higher-dimensional maps possessing the Laurent property and demonstrating int
Externí odkaz:
http://arxiv.org/abs/2402.18310
Autor:
Hone, Andrew N. W.
A Heron triangle is one that has all integer side lengths and integer area, which takes its name from Heron of Alexandria's area formula. From a more relaxed point of view, if rescaling is allowed, then one can define a Heron triangle to be one whose
Externí odkaz:
http://arxiv.org/abs/2401.05581
Publikováno v:
Open Communications in Nonlinear Mathematical Physics, Special Issue in Memory of Decio Levi (February 15, 2024) ocnmp:12491
In recent work, we presented the construction of a family of difference equations associated with the Stieltjes continued fraction expansion of a certain function on a hyperelliptic curve of genus $g$. As well as proving that each such discrete syste
Externí odkaz:
http://arxiv.org/abs/2310.19584
Publikováno v:
Nonlinearity 37 095028 (2024)
Recently Gubbiotti, Joshi, Tran and Viallet classified birational maps in four dimensions admitting two invariants (first integrals) with a particular degree structure, by considering recurrences of fourth order with a certain symmetry. The last thre
Externí odkaz:
http://arxiv.org/abs/2309.02336
We consider the scaling similarity solutions of two integrable cubically nonlinear partial differential equations (PDEs) that admit peaked soliton (peakon) solutions, namely the modified Camassa-Holm (mCH) equation and Novikov's equation. By making u
Externí odkaz:
http://arxiv.org/abs/2205.14767
Autor:
Barnes, Lucy E., Hone, Andrew N. W.
The $b$-family is a one-parameter family of Hamiltonian partial differential equations of non-evolutionary type, which arises in shallow water wave theory. It admits a variety of solutions, including the celebrated peakons, which are weak solutions i
Externí odkaz:
http://arxiv.org/abs/2201.00265
Autor:
Hone, Andrew N. W.
Recently Ovsienko and Tabachnikov considered extensions of Somos and Gale-Robinson sequences, defined over the algebra of dual numbers. Ovsienko used the same idea to construct so-called shadow sequences derived from other nonlinear recurrence relati
Externí odkaz:
http://arxiv.org/abs/2111.10905
Autor:
Hone, Andrew N. W.
We consider the growth rate of the Mahler measure in discrete dynamical systems with the Laurent property, and in cluster algebras, and compare this with other measures of growth. In particular, we formulate the conjecture that the growth rate of the
Externí odkaz:
http://arxiv.org/abs/2109.08217