A note on iterated maps of the unit sphere

DOI10.1007/s00010-023-00979-6arXiv2301.11159OpenAlexW4385543949MaRDI QIDQ6130588

Chaitanya Gopalakrishna

Publication date: 3 April 2024

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2301.11159

zbMATH Keywords

degreeunit spheresingular homology groupiterative rootDevaney chaositerated map

Mathematics Subject Classification ID

Iteration theory, iterative and composite equations (39B12) Dynamics in general topological spaces (37B02)

Cites Work

• General theorem for the existence of iterative roots of homeomorphisms with periodic points
• Typical continuous functions are not iterates
• On a factorization of homeomorphisms of the circle possessing periodic points
• Iterative roots of some homeomorphisms with a rational rotation number
• Recent results on iteration theory: iteration groups and semigroups in the real case
• The Set of Second Iterates is Nowhere Dense in C
• The Borel structure of iterates of continuous functions
• Some Dual Statements Concerning Wiener Measure and Baire Category
• When is f(f(z)) = az 2 + bz + c?
• The Set of all Iterates is Nowhere Dense in C([ 0, 1 , [ 0, 1 ])]
• Period Three Implies Chaos
• PM functions, their characteristic intervals and iterative roots
• Dynamics of the iteration operator on the space of continuous self-maps
• Approximations of continuous functions by squares
• Recent results on functional equations in a single variable, perspectives and open problems
• The non-iterates are dense in the space of continuous self-maps
• Iterative square roots of functions
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