{"title":"Chaos in periodically forced reversible vector fields","authors":"I. Labouriau, Elisa Sovrano","doi":"10.5427/jsing.2020.22p","DOIUrl":"https://doi.org/10.5427/jsing.2020.22p","url":null,"abstract":"We discuss the appearance of chaos in time-periodic perturbations of reversible vector fields in the plane. We use the normal forms of codimension~$1$ reversible vector fields and discuss the ways a time-dependent periodic forcing term of pulse form may be added to them to yield topological chaotic behaviour. Chaos here means that the resulting dynamics is semi-conjugate to a shift in a finite alphabet. \u0000The results rely on the classification of reversible vector fields and on the theory of topological horseshoes. This work is part of a project of studying periodic forcing of symmetric vector fields.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"237 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77497288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the topology of non-isolated real singularities","authors":"N. Dutertre","doi":"10.5427/jsing.2020.22j","DOIUrl":"https://doi.org/10.5427/jsing.2020.22j","url":null,"abstract":"Khimshiashvili proved a topological degree formula for the Eu-ler characteristic of the Milnor fibres of a real function-germ with an isolated singularity. We give two generalizations of this result for non-isolated singularities. As corollaries we obtain an algebraic formula for the Euler characteristic of the fibres of a real weighted-homogeneous polynomial and a real version of the L{^e}-Iomdine formula. We have also included some results of the same flavor on the local topology of locally closed definable sets.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"63 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2019-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85962638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Milnor Fiber Boundary of a Quasi-Ordinary Surface","authors":"G. Kennedy, Lee J. McEwan","doi":"10.5427/JSING.2019.19C","DOIUrl":"https://doi.org/10.5427/JSING.2019.19C","url":null,"abstract":"We give a recursive formula, expressed in terms of the characteristic tuples, for the Betti numbers of the boundary of the Milnor fiber of an irreducible quasi-ordinary surface. The singular locus of the surface consists of two components, and for each component we introduce a sequence of increasingly simpler surfaces. Our recursion depends on a detailed comparison of these two sequences. In the final section, we indicate how we expect pieces of these associated surfaces to glue together to reconstruct the Milnor fiber and its boundary.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"7 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76833587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Middle multiplicative convolution and hypergeometric equations","authors":"Nicolas Martin","doi":"10.5427/jsing.2021.23k","DOIUrl":"https://doi.org/10.5427/jsing.2021.23k","url":null,"abstract":"Using a relation due to Katz linking up additive and multiplicative convolutions, we make explicit the behaviour of some Hodge invariants by middle multiplicative convolution, following [DS13] and [Mar18a] in the additive case. Moreover, the main theorem gives a new proof of a result of Fedorov computing the Hodge invariants of hypergeometric equations.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"2 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85301093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Symmetries of special 2-flags","authors":"P. Mormul, F. Pelletier","doi":"10.5427/jsing.2020.21k","DOIUrl":"https://doi.org/10.5427/jsing.2020.21k","url":null,"abstract":"This work is a continuation of authors' research interrupted in the year 2010. Derived are recursive relations describing for the first time all infinitesimal symmetries of special 2-flags (sometimes also misleadingly called `Goursat 2-flags'). When algorithmized to the software level, they will give an answer filling in the gap in knowledge as of 2010: on one side the local finite classification of special 2-flags known in lengths not exceeding four, on the other side the existence of a continuous numerical modulus of that classification in length seven.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"6 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74049438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Recognition Problem of Frontal Singularities","authors":"G. Ishikawa","doi":"10.5427/jsing.2020.21i","DOIUrl":"https://doi.org/10.5427/jsing.2020.21i","url":null,"abstract":"This is a survey article on recognition problem of frontal singularities. We specify geometrically several frontal singularities and then we solve the recognition problem of such singularities, giving explicit normal forms. We combine the recognition results by K. Saji and several arguments on openings, which was performed for the classification of singularities of tangent surfaces (tangent developables) by the author. As an application of our solutions of recognition problem of frontal singularities, we announce the classification of singularities appearing in tangent surfaces of generic null curves which are ruled by null geodesics in general Lorentz three-manifolds, mentioning related recognition results and open problems.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"31 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87259705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R. S. Carvalho, B. Oréfice-Okamoto, J. N. Tomazella
{"title":"$mu$-constant deformations of functions on an ICIS","authors":"R. S. Carvalho, B. Oréfice-Okamoto, J. N. Tomazella","doi":"10.5427/jsing.2019.19i","DOIUrl":"https://doi.org/10.5427/jsing.2019.19i","url":null,"abstract":"We study deformations of holomorphic function germs $f:(X,0)tomathbb C$ where $(X,0)$ is an ICIS. We present conditions for these deformations to have constant Milnor number, Euler obstruction and Bruce-Roberts number.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"144 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75996591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Kato's chaos created by quadratic mappings associated with spherical orthotomic curves","authors":"T. Nishimura","doi":"10.5427/jsing.2020.21l","DOIUrl":"https://doi.org/10.5427/jsing.2020.21l","url":null,"abstract":"Singular quadratic mappings creating Kato’s chaos are given.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"7 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89357171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quasi-periodic motions on symplectic tori","authors":"M. Garay, A. Kessi, D. Straten, N. Yousfi","doi":"10.5427/jsing.2023.26c","DOIUrl":"https://doi.org/10.5427/jsing.2023.26c","url":null,"abstract":"The results of Kolmogorov, Arnold, and Moser on the stability of quasi-periodic motions spanning lagrangian tori in Hamiltonian systems are of fundamental importance and led to the development of KAM theory. Over the years, many variations of these results on quasi-periodic motions have been considered. In this paper, we present a more conceptual way of attacking such problems by considering the particular case of quasi-periodic motions on symplectic tori.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"5 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89059540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Jet Bundles on Gorenstein Curves and Applications","authors":"Letterio Gatto, Andrea T. Ricolfi","doi":"10.5427/jsing.2020.21d","DOIUrl":"https://doi.org/10.5427/jsing.2020.21d","url":null,"abstract":"In the last twenty years a number of papers appeared aiming to construct locally free replacements of the sheaf of principal parts for families of Gorenstein curves. The main goal of this survey is to present to the widest possible audience of mathematical readers a catalogue of such constructions, discussing the related literature and reporting on a few applications to classical problems in Enumerative Algebraic Geometry.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"30 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78082766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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