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http://hdl.handle.net/1942/39889
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DC Field | Value | Language |
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dc.contributor.author | Jardón-Kojakhmetov, Hildeberto | - |
dc.contributor.author | HUZAK, Renato | - |
dc.date.accessioned | 2023-03-30T10:02:29Z | - |
dc.date.available | 2023-03-30T10:02:29Z | - |
dc.date.issued | 2023 | - |
dc.date.submitted | 2023-03-23T08:34:25Z | - |
dc.identifier.citation | BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 29 (3) , p. 371 -388 | - |
dc.identifier.issn | 1370-1444 | - |
dc.identifier.uri | http://hdl.handle.net/1942/39889 | - |
dc.description.abstract | The goal of this paper is to study global dynamics of C∞-smooth slow-fast systems on the 2-torus of class C∞ using geometric singular perturbation theory and the notion of slow divergence integral. Given any m ∈ N and two relatively prime integers k and l, we show that there exists a slow-fast system Yϵ on the 2-torus that has a 2m-link of type (k, l), i.e. a (disjoint finite) union of 2m slow-fast limit cycles each of (k, l)-torus knot type, for all small ϵ > 0. The (k, l)-torus knot turns around the 2-torus k times meridionally and l times longitudinally. There are exactly m repelling limit cycles and m attracting limit cycles. Our analysis: a) proves the case of normally hyperbolic singular knots, and b) provides sufficient evidence to conjecture a similar result in some cases where the singular knots have regular nilpotent contact with the fast foliation. | - |
dc.description.sponsorship | The authors thank the anonymous reviewer for the constructive feedback provided, which helped to improve our manuscript. | - |
dc.language.iso | en | - |
dc.publisher | BELGIAN MATHEMATICAL SOC TRIOMPHE | - |
dc.subject.other | Slow-fast systems | - |
dc.subject.other | torus knots | - |
dc.subject.other | limit cycles | - |
dc.subject.other | slow divergence integral | - |
dc.title | Slow-fast torus knots | - |
dc.type | Journal Contribution | - |
dc.identifier.epage | 388 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | 371 | - |
dc.identifier.volume | 29 | - |
local.bibliographicCitation.jcat | A1 | - |
local.publisher.place | CP 218,01 BOULEVARD TRIOMPE, B 1050 BRUSSELS, BELGIUM | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
dc.identifier.doi | https://doi.org/10.36045/j.bbms.220208 | - |
dc.identifier.isi | 000965201100005 | - |
dc.identifier.url | https://projecteuclid.org/journals/bulletin-of-the-belgian-mathematical-society-simon-stevin/volume-29/issue-3 | - |
dc.identifier.eissn | 2034-1970 | - |
local.provider.type | - | |
local.uhasselt.international | yes | - |
item.fullcitation | Jardón-Kojakhmetov, Hildeberto & HUZAK, Renato (2023) Slow-fast torus knots. In: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 29 (3) , p. 371 -388. | - |
item.accessRights | Restricted Access | - |
item.fulltext | With Fulltext | - |
item.contributor | Jardón-Kojakhmetov, Hildeberto | - |
item.contributor | HUZAK, Renato | - |
crisitem.journal.issn | 1370-1444 | - |
crisitem.journal.eissn | 2034-1970 | - |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
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Slow_fast_Torus_Knots.pdf Restricted Access | Peer-reviewed author version | 4.33 MB | Adobe PDF | View/Open Request a copy |
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