Dirac physical measures for generic diffeomorphisms
Bruno Santiago
TL;DR
This paper proves that for most smooth dynamical systems, the only stable fixed points with widespread influence are sinks, meaning they attract nearby points and have dense basins of attraction.
Contribution
It establishes that, generically, Dirac physical measures with dense basins are exclusively supported on sinks in $C^1$ diffeomorphisms.
Findings
Dirac physical measures with dense basins are supported on sinks.
Generic $C^1$ diffeomorphisms have this property.
Non-sink Dirac measures do not have dense basins.
Abstract
We prove that, for a generic diffeomorphism, the only Dirac physical measures with dense statistical basin are those supported on sinks.
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Taxonomy
TopicsAdvanced Thermodynamics and Statistical Mechanics · Advanced Operator Algebra Research · Cosmology and Gravitation Theories