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Poincaré-birkhoff Theorems in Random Dynamics
| Content Provider | Semantic Scholar |
|---|---|
| Author | Rezakhanlou, Álvaro Pelayo Fraydoun |
| Copyright Year | 2013 |
| Abstract | We propose a generalization of the Poincaré-Birkhoff Theorem on area-preserving twist maps to area-preserving twist maps F that are random with respect to an ergodic probability measure. In this direction, we will prove several theorems concerning existence, density, and type of the fixed points. To this end first we introduce a randomized version of generalized generating functions, and verify the correspondence between its critical points and the fixed points of F , a fact which we successively exploit in order to prove the theorems. The study we carry out needs to combine probabilistic techniques with methods from nonlinear PDE, and from differential geometry, notably Moser’s method and Conley-Zehnder theory. Our stochastic model in the periodic case coincides with the classical setting of the Poincaré-Birkhoff Theorem. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://math.berkeley.edu/~rezakhan/finalstationtwist.pdf |
| Alternate Webpage(s) | http://math.berkeley.edu/~rezakhan/finalstationtwist.pdf |
| Alternate Webpage(s) | http://www.math.ucsd.edu/~alpelayo/Docs/stationarytwist55.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Birkhoff interpolation Conley index theory Conley–Zehnder theorem Ergodicity Fixed point (mathematics) Generalization (Psychology) Map Moser spindle Nonlinear system Randomized algorithm |
| Content Type | Text |
| Resource Type | Article |
