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Nowhere coexpanding functions
Andrew Cook1, Andy Hammerlindl1, Warwick Tucker1
1School of Mathematics, Monash University, Victoria 3800, Australia.
Chaos (Woodbury, N.Y.)
|December 4, 2023
Summary
Researchers defined nowhere coexpanding functions, a class of C1 functions closed under composition. This work generalizes Singer
Area of Science:
- Mathematical analysis
- Dynamical systems theory
Background:
- The study of iterated functions and their fixed points is crucial in dynamical systems.
- Understanding the properties of functions with specific derivative characteristics, like non-positive Schwarzian derivatives, is an active research area.
Purpose of the Study:
- To introduce and define a new class of functions termed "nowhere coexpanding functions."
- To investigate the composition properties of this new function family.
- To analyze the fixed points of nowhere coexpanding functions and generalize existing theorems.
Main Methods:
- Definition of a novel class of C1 functions: nowhere coexpanding functions.
- Demonstration that this class is closed under function composition.
- Application of analytical techniques to study the fixed points of these functions.
Main Results:
- A new family of C1 functions, nowhere coexpanding functions, is formally defined.
- This family is shown to be closed under composition.
- Results concerning the number and nature of fixed points are established, generalizing Singer's theorem.
Conclusions:
- The newly defined nowhere coexpanding functions possess unique properties regarding composition and fixed points.
- The findings extend classical results in the theory of dynamical systems and function iteration.
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