Piecewise smooth vector fields: Closing Lemmas, shifts and horseshoe dynamics.
Closing lemmas and shifts for piecewise smooth vector fields
Limit cycles of discontinuous piecewise smooth differential systems in the plane R...
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| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Ecole Normale Super, DMA, UMR 8553, F-75005 Paris - France
[2] USP, ICMC, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 23, n. 3, p. 685-703, MAR 2009. |
| Web of Science Citations: | 8 |
| Abstract | |
In the space of C-k piecewise expanding unimodal maps, k >= 1, we characterize the C-1 smooth families of maps where the topological dynamics does not change ( the ``smooth deformations{''}) as the families tangent to a continuous distribution of codimension-one subspaces (the ``horizontal{''} directions) in that space. Furthermore such codimension-one subspaces are defined as the kernels of an explicit class of linear functionals. As a consequence we show the existence of Ck-1+(Lip) deformations tangent to every given C-k horizontal direction, for k >= 2. (AU) | |
| FAPESP's process: | 03/03107-9 - Qualitative theory of differential equations and singularity theory |
| Grantee: | Carlos Teobaldo Gutierrez Vidalon |
| Support Opportunities: | Research Projects - Thematic Grants |