On the self-similarity problem for smooth flows on orientable surfaces
Joanna Ku{\l}aga
TL;DR
This paper constructs a class of smooth flows on orientable surfaces of genus greater than one that lack self-similarities, addressing a specific problem in dynamical systems.
Contribution
It introduces a new class of flows on higher-genus surfaces that are proven to have no self-similarities, advancing understanding in the field of smooth dynamical systems.
Findings
Existence of flows without self-similarities on certain surfaces
Construction method for such flows
Implications for the study of dynamical symmetries
Abstract
On each compact, connected, orientable surface of genus greater than one we construct a class of flows without self-similarities.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometric Analysis and Curvature Flows · Stochastic processes and statistical mechanics