First return path systems: Differentiability, continuity, and orderings
type: Item
instance of: scholarly article
title: First return path systems: Differentiability, continuity, and orderings
zbMATH Open document ID: 0821.26006
DOI: 10.1007/BF01874355
author: Udayan B. Darji
author: Michael J. Evans
author: Richard J. O'Malley
published in: Acta Mathematica Hungarica
publication date: 1995-09-11T00:00:00Z
review text: The study of first return path systems is continued. If \(f: [0, 1]\to \mathbb{R}\) is compositely differentiable to \(g\) and if for each \(x\in [0, 1]\quad g(x)\) is a bilateral derived number of \(f\) at \(x\) then \(f\) is universally first return differentiable to \(g\). A function \(f\) is first return continuous iff \(f\) is \(\text{DB}_ 1\). If \(f\in \text{DB}^*_ 1\) then \(f\) is universally first return continuous. Some examples are shown and it is proven that each first return path system can be generated from a trajectory of a continuous transitive mapping.
Mathematics Subject Classification ID: 26A24
Mathematics Subject Classification ID: 26A27
Mathematics Subject Classification ID: 26A15
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 26A18
zbMATH DE Number: 755494
zbMATH Keywords: first return differentiation
zbMATH Keywords: first return path systems
zbMATH Keywords: compositely differentiable
zbMATH Keywords: first return continuous
zbMATH Keywords: trajectory
reviewed by: Zbigniew Grande
MaRDI profile type: Publication
cites work: Representations of Functions by Derivatives
cites work: Differentiation of real functions
cites work: Path Derivatives: A Unified View of Certain Generalized Derivatives
cites work: A Note on a Darboux Continuous Function
cites work: Decomposition of Peano Derivatives
cites work: On approximate Peano derivatives
cites work: Baire 1 functions, approximately continuous functions and derivatives
cites work: Q5844594
cites work: Darboux Functions of Baire Class One and Derivatives
cites work: Baire ∗ 1, Darboux Functions
cites work: Selective derivates
cites work: Decomposition of Approximate Derivatives
cites work: First Return Path Derivatives
cites work: Selective, bi-selective, and composite differentiation
cites work: Maximoff's theorem
full work available at URL: https://doi.org/10.1007/bf01874355
OpenAlex ID: W1974512164
description: scientific article; zbMATH DE number 755494