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Nowhere coexpanding functions.

Andrew Cook1, Andy Hammerlindl1, Warwick Tucker1

  • 1School of Mathematics, Monash University, Victoria 3800, Australia.

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Summary
This summary is machine-generated.

Researchers defined nowhere coexpanding functions, a class of C1 functions closed under composition. This work generalizes Singer

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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.