Hierarchical Gompertzian growth maps with application in astrophysics

TL;DR

This paper introduces hierarchical Gompertzian growth maps that model discrete scales in systems, demonstrating their ability to generate all observed astrophysical length and mass scales.

Contribution

The paper develops a new class of hierarchical maps based on Gompertzian growth, providing general solutions and applying them to astrophysical scale modeling.

Findings

Maps generate all observed astrophysical length scales.

Maps produce all observed astrophysical mass scales.

The model captures complex growth phenomena.

Abstract

The Gompertz model describes the growth in time of the size of significant quantities associated to a large number of systems, taking into account nonlinearity features by a linear equation satisfied by a nonlinear function of the size. Following this scheme, we introduce a class of hierarchical maps which describe discrete sequences of intermediate characteristic scales. We find the general solutions of the maps, which account for a rich set of possible phenomena. Eventually, we provide an important application, by showing that a map belonging to the class so introduced generates all the observed astrophysical length and mass scales.