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Research Article
Discrete Dynamics in Nature and Society
Volume 2018 (2018), Article ID 4269121, 2 pages
https://doi.org/10.1155/2018/4269121
Corrigendum

Corrigendum to “A Note on Discrete Multitime Recurrences of Samuelson-Hicks Type”

1Department of Law and Economics, University Mediterranea of Reggio Calabria, Reggio Calabria, Italy
2Decisions Lab, University Mediterranea of Reggio Calabria, Reggio Calabria, Italy
3Department of Economics and Statistics, University of Siena, Siena, Italy

Correspondence should be addressed to Francesco Strati; ti.crinu@itarts.ocsecnarf

Received 16 August 2017; Accepted 7 December 2017; Published 15 January 2018

Copyright © 2018 Bruno Antonio Pansera and Francesco Strati. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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This corrigendum is intended to make it clear that our contribution [1] is a note on the economic meaning of the unpublished work titled “A Multitime Recurrences of Samuelson-Hicks Type” by C. Ghiu, C. Udrişte, and R. Tuligǎ which could not be properly cited because of an editorial rule of the journal about unpublished papers.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of the Floquet theory can be found in [2]; in [1], we discussed a further possible extension proposed by the unpublished work titled “A Multitime Recurrences of Samuelson-Hicks Type” by C. Ghiu, C. Udrişte, and R. Tuligǎ.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].

References

  1. B. A. Pansera and F. Strati, “A note on discrete multitime recurrences of Samuelson-Hicks type,” Discrete Dynamics in Nature and Society, vol. 2016, Article ID 6891302, 4 pages, 2016. View at Publisher · View at Google Scholar · View at Scopus
  2. P. v. Mouche and W. Heijman, “Floquet theory and economic dynamics (extended version),” Wageningen Economic Papers, 1996.
  3. C. Ghiu, C. Udriste, and R. Tuligǎ, “Tuligǎ Discrete, multitime recurrences and discrete minimal submanifolds,” Balkan Journal of Geometry and Its Applications, vol. 20, no. 1, pp. 49–64, 2015. View at Google Scholar
  4. C. Ghiu, C. Udriste, and R. Tuligǎ, “Discrete multitime recurrences and their application in economics,” in Proceedings of the The VIII-th International Conference: Differential Geometry and Dynamical Systems (DGDS-2014), Mangalia , Romania, 2014.
  5. C. Ghiu, R. Tuligǎ, and C. Udriste, “Discrete multitime multiple recurrence,” 2015, https://arxiv.org/abs/1506.02508.
  6. C. Ghiu, C. Udriste, and R. Tuligǎ, “Linear discrete multitime multiple recurrence,” Analysis of PDEs, 2015. View at Google Scholar
  7. C. Ghiu, C. Udriste, I. Tevy, and R. Tuligǎ, “Multitime Samuelson-Hicks diagonal recurrence,” BSG Proceedings, Geometry Balkan Press, 2015.