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Genericity of historic behavior for maps and flows
| Content Provider | Scilit |
|---|---|
| Author | Carvalho, Maria Varandas, Paulo |
| Copyright Year | 2021 |
| Description | Journal: Nonlinearity We establish a sufficient condition for a continuous map, acting on a compact metric space, to have a Baire residual set of points exhibiting historic behavior (also known as irregular points). This criterion applies, for instance, to a minimal and non-uniquely ergodic map; to maps preserving two distinct probability measures with full support; to non-trivial homoclinic classes; to some non-uniformly expanding maps; and to partially hyperbolic diffeomorphisms with two periodic points whose stable manifolds are dense, including Mañé and Shub examples of robustly transitive non-hyperbolic diffeomorphisms. This way, our unifying approach recovers a collection of known deep theorems on the genericity of the irregular set, for both additive and sub-additive potentials, and also provides a number of new applications. |
| Related Links | https://iopscience.iop.org/article/10.1088/1361-6544/ac1f77/pdf |
| Ending Page | 7044 |
| Page Count | 15 |
| Starting Page | 7030 |
| ISSN | 09517715 |
| e-ISSN | 13616544 |
| DOI | 10.1088/1361-6544/ac1f77 |
| Journal | Nonlinearity |
| Issue Number | 10 |
| Volume Number | 34 |
| Language | English |
| Publisher | IOP Publishing |
| Publisher Date | 2021-09-07 |
| Access Restriction | Open |
| Subject Keyword | Journal: Nonlinearity Mathematical Social Sciences Hyperbolic Diffeomorphisms Historic Behavior Additive and Sub |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Statistical and Nonlinear Physics Mathematical Physics |
