1. Introduction
This corrigendum is intended to make it clear that our contribution [1] is a note on the economic meaning of the unpublished work titled “A Multitime Recurrences of Samuelson-Hicks Type” by C. Ghiu, C. Udrişte, and R. Tuligǎ which could not be properly cited because of an editorial rule of the journal about unpublished papers. From this article, the aim of our note is to set forth an interpretation of the economic meaning of the model so as to trigger further research on the topic.
This paper stems from the works of Professor C. Udrişte who set up this topic in the cited paper and suggested to us the term sheet of time rather than the original leaf of time. The contribution to the literature by Professor C. Udrişte to the argument is rich: this addendum recognizes the crucial contribution of him and his collaborators for the first development of the topic by making clear the chronology of the relevant contributions.
2. Genesis of Multitime Recurrences in Economics
In Floquet theory, it is necessary to find the associated monodromy matrix and its eigenvalues (called Floquet multipliers) in order to pass from a constant coefficient state to a periodic one. It can be crucial in a recurrence formulation (as noted in [2]) in which time-independent coefficients are unrealistic. An application of the Floquet theory can be found in [2]; in [1], we discussed a further possible extension proposed by the unpublished work titled “A Multitime Recurrences of Samuelson-Hicks Type” by C. Ghiu, C. Udrişte, and R. Tuligǎ. In this case, there is a generalization of the periodicity to a sheet of time rather than a point of time approach. In few words, it can be stated that, by a multitime approach, a point of time opens up to a vector of multiple times at that date.
2.1. Chronology
As far as we know, [2] firstly applied the recurrence formulation by taking into account the so-called floquetization. Then, the model has been generalized by means of multitime recurrences. In particular, following the model set up in [3], there has been a first application to economics in [4]. Moreover, in [5, 6], there are some studied problems on multitime multiple recurrence equations and linear recurrences with constant coefficients. An important contribution is the application to the Samuelson-Hicks model in [7], which applies the multitime diagonal recurrences. Furthermore, in [1], we tried to clarify the sound meaning of the multitime approach applied to the Samuelson-Hicks model as in [7].