The bifurcation set as a topological invariant for one-dimensional dynamics
| Autor: | Gabriel Fuhrmann, Maik Gröger, Alejandro Passeggi |
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| Přispěvatelé: | Fuhrmann Gabriel, Gröger Maik, Passeggi Alejandro, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Transitive relation
topological invariants Applied Mathematics 010102 general mathematics one-dimensional dynamics General Physics and Astronomy Statistical and Nonlinear Physics Dynamical Systems (math.DS) Interval (mathematics) Topological entropy Topology 01 natural sciences 010101 applied mathematics Set (abstract data type) Perspective (geometry) FOS: Mathematics open systems bifurcation set/locus Mathematics - Dynamical Systems 0101 mathematics Invariant (mathematics) Mathematical Physics Bifurcation Mathematics Unit interval |
| Zdroj: | COLIBRI Universidad de la República instacron:Universidad de la República Nonlinearity, 2021, Vol.34(3), pp.1366 [Peer Reviewed Journal] |
| Popis: | For a continuous map on the unit interval or circle, we define the bifurcation set to be the collection of those interval holes whose surviving set is sensitive to arbitrarily small changes of their position. By assuming a global perspective and focusing on the geometric and topological properties of this collection rather than the surviving sets of individual holes, we obtain a novel topological invariant for one-dimensional dynamics. We provide a detailed description of this invariant in the realm of transitive maps and observe that it carries fundamental dynamical information. In particular, for transitive non-minimal piecewise monotone maps, the bifurcation set encodes the topological entropy and strongly depends on the behavior of the critical points. 20 pages, 3 figures |
| Databáze: | OpenAIRE |
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