[seqfan] Re: Higher dimensional analogues to plane division by ellipses?

[allouche at math.jussieu.fr]

Thanks for pointing out Spinadel 1997!

For the papers you cite below, I could access only
[30], where it seems that the expression "metallic mean"
is not used.
Is it used (explicitly) in the other four papers?

best
jp


Hans Havermann <gladhobo at teksavvy.com> a écrit :

> Yes, thank you. Spinadel's 1999 'The Family of Metallic Means' <   
> http://www.mi.sanu.ac.rs/vismath/spinadel/ > with its bibliography   
> of 30 references, interestingly has a 1997 precursor (The Family of   
> Metallic Means in Design) with *additional* references, including:
>
> [28] Godfrey Gumbs and M. K. Ali, Dynamical Maps, Cantor Spectra,   
> and Localization for Fibonacci and Related Quasiperiodic Lattices,   
> Phys. Rev. Lett., vol. 60, 1988.
>
> [29] Godfrey Gumbs and M. K. Ali, Quasiperiodic dynamics for a   
> generalized third-order Fibonacci series, Physical Review B, vol.   
> 38, Nr. 10, october 1988.
>
> [30] Godfrey Gumbs and M. K. Ali , Electronic Properties of the   
> Tight-Binding Fibonacci Hamiltonian, J. Phys. A: Math. Gen. vol. 22,  
>  1989.
>
> [31] Kolár M. and M. K. Ali, Generalized Fibonacci superlattices,   
> dynamical trace maps, and magnetic excitations, Phys. Rev. B, vol.   
> 39, Nr. 1, 1989.
>
> [32] Kolár M. and M. K. Ali, Attractors in quantum Ising models,   
> Phys. Rev. B, vol. 40, Nr. 16, 1989.
>
> Reference 31 < http://prb.aps.org/abstract/PRB/v39/i1/p426_1 >   
> mentions "spin-wave spectra for Fibonacci superlattices with copper   
> and nickel mean are compared with those for the golden-mean case".
>
>
> On Jun 2, 2013, at 12:54 PM, allouche at math.jussieu.fr wrote:
>
>> It is that clear that the expression "metallic mean"
>> was coined in 1999?
>>
>> I seem to remember having heard the expression
>> "metallic mean" before (i.e., some years after
>> the discovery of quasicrystals).
>>
>> In particular I traced back a 1996 paper:
>> J. A. G. Roberts, Escaping orbits in trace maps,
>> Physica A: Statistical Mechanics and its Applications,
>> Volume 228, Issues 1?4, 15 June 1996, Pages 295--325
>> where the term "metallic mean" is used (see Page 298
>> just before (11)). In that paper "metallic-mean" sequences
>> are generated by the substitution rule (morphism of the
>> free monoid) a --> b, b --> b^{\ell} a, whose transition
>> matrix admits (1 + \sqrt{1+4\ell})/2 as dominant eigenvalue.
>>
>> Other "metals" were used before, e.g., bronze in several
>> papers including
>> G. Gumbs and M. K. Ali, Scaling and eigenstates for a class of
>> one-dimensional quasiperiodic lattices, J. Phys. A: Math. Gen.
>> 1988, 21 L517--L521.
>>
>> I am not even sure that Roberts' paper is the first one where
>> the expression is used
>
>
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