A uniform ergodic theorem for degenerate flows on the annulus Article Swipe
Jonathan Ben-Artzi
,
Baptiste Morisse
·
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1902.06681
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1902.06681
Motivated by the well-known phase-space portrait of the nonlinear pendulum, the purpose of this paper is to obtain convergence rates in the ergodic theorem for flows in the plane that have arbitrarily slow trajectories. Considering bounded periodic trajectories near the heteroclinic orbits, it is shown that despite lacking a spectral gap, there exists a functional space (which is a strict subset of $L^2$) on which time averages converge uniformly to spatial averages (with an explicit rate). The main ingredient of the proof is an estimate of the density of the spectrum of the generator of the flow near zero.
Related Topics
Concepts
Ergodic theory
Mathematics
Bounded function
Annulus (botany)
Mathematical analysis
Phase portrait
Uniform boundedness
Phase space
Rate of convergence
Generator (circuit theory)
Degenerate energy levels
Nonlinear system
Pure mathematics
Bifurcation
Physics
Channel (broadcasting)
Electrical engineering
Botany
Thermodynamics
Power (physics)
Engineering
Biology
Quantum mechanics
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/1902.06681
- https://arxiv.org/pdf/1902.06681
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4381707872
All OpenAlex metadata
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https://openalex.org/W4381707872Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.1902.06681Digital Object Identifier
- Title
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A uniform ergodic theorem for degenerate flows on the annulusWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2019Year of publication
- Publication date
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2019-02-18Full publication date if available
- Authors
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Jonathan Ben-Artzi, Baptiste MorisseList of authors in order
- Landing page
-
https://arxiv.org/abs/1902.06681Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/1902.06681Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/1902.06681Direct OA link when available
- Concepts
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Ergodic theory, Mathematics, Bounded function, Annulus (botany), Mathematical analysis, Phase portrait, Uniform boundedness, Phase space, Rate of convergence, Generator (circuit theory), Degenerate energy levels, Nonlinear system, Pure mathematics, Bifurcation, Physics, Channel (broadcasting), Electrical engineering, Botany, Thermodynamics, Power (physics), Engineering, Biology, Quantum mechanicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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