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Barge, HCorresponding Author

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January 1, 2026
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On the Growth Rate Inequality for Self-Maps of the Sphere

Publicated to: INDIANA UNIVERSITY MATHEMATICS JOURNAL. 74 (4): 1007-1022 - 2025-01-01 74(4), DOI: 10.1512/iumj.2025.74.60250

Authors:

Barge, H; Hernández-Corbato, L
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Affiliations

Univ Complutense Madrid, Fac Ciencias Matemat - Author
Univ Politecnica Madrid, ETS Ingenieros Informat - Author

Abstract

Let Sm = {x02 + x12 + < middle dot >< middle dot >+ x2m = 1} and P = {x0 = x1 = 0} boolean AND Sm. Suppose f is a self-map of Sm such that f-1(P) = P and | deg(f|P )|< | deg(f)|. Then, the number of fixed points of f n grows at least exponentially with base |d|> 1, where d = deg(f)/ deg(f|P) is an element of Z.
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Keywords

Growth rate inequalityPeriodic pointPeriodic pointsTopological degree

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal INDIANA UNIVERSITY MATHEMATICS JOURNAL due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2025, it was in position 84/492, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics.

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Impact and social visibility

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • Assignment of a Handle/URN as an identifier within the deposit in the Institutional Repository: https://oa.upm.es/93925/

As a result of the publication of the work in the institutional repository, statistical usage data has been obtained that reflects its impact. In terms of dissemination, we can state that, as of

  • Views: 22
  • Downloads: 14
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Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (BARGE YAÑEZ, HECTOR) .

the author responsible for correspondence tasks has been BARGE YAÑEZ, HECTOR.

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Project objectives

La aportación persigue los siguientes objetivos: analizar la desigualdad en la tasa de crecimiento para autoaplicaciones de la esfera Sm; caracterizar las condiciones bajo las cuales el número de puntos fijos de las iteraciones fn crece exponencialmente; determinar la relación entre los grados de la autoaplicación f y su restricción a un subconjunto P; evaluar el impacto del cociente d = deg(f)/deg(f|P) en el crecimiento del número de puntos fijos; y establecer criterios matemáticos que garanticen que la base de crecimiento |d| sea mayor que 1.
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Most relevant results

El estudio aborda la desigualdad en la tasa de crecimiento para autoaplicaciones de la esfera Sm bajo ciertas condiciones topológicas. Los resultados más relevantes son: (1) Se define Sm como la esfera unidad en dimensión m y P como la intersección booleana de Sm con el plano {x0 = x1 = 0}. (2) Se considera una autoaplicación f de Sm que cumple f-1(P) = P y la desigualdad |deg(f|P)| < |deg(f)|. (3) Se demuestra que el número de puntos fijos de la iteración fn crece al menos exponencialmente con base |d| > 1, donde d = deg(f)/deg(f|P) es un entero. Estos resultados cuantifican la dinámica de puntos fijos en función de los grados de las restricciones de f.
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