{"id":22,"date":"2015-12-01T01:49:09","date_gmt":"2015-12-01T01:49:09","guid":{"rendered":"http:\/\/www.ime.unicamp.br\/~ddnovaes\/?page_id=22"},"modified":"2024-09-27T11:30:06","modified_gmt":"2024-09-27T11:30:06","slug":"inicio","status":"publish","type":"page","link":"https:\/\/www.ime.unicamp.br\/~ddnovaes\/","title":{"rendered":""},"content":{"rendered":"
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Artigos Selecionado<\/strong><\/em><\/span><\/h2>\n
(clique aqui<\/a>\u00a0para uma lista completa)<\/h5>\n
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Pedro C. Pereira; Douglas D. Novaes; Murilo R. C\u00e2ndido<\/p>

A mechanism for detecting normally hyperbolic invariant tori in differential equations<\/a> Journal Article<\/span> <\/p>

Em: <\/span>Journal de Math\u00e9matiques Pures et Appliqu\u00e9es, <\/span>vol. 177, <\/span>n\u00e3o 1, <\/span>pp. 45, <\/span>2023<\/span>.<\/p>

Resumo<\/a><\/span> | Links<\/a><\/span> | BibTeX<\/a><\/span><\/p>

@article{PerNovCan23,
\r\ntitle = {A mechanism for detecting normally hyperbolic invariant tori in differential equations},
\r\nauthor = {Pedro C. Pereira and Douglas D. Novaes and Murilo R. C\u00e2ndido},
\r\nurl = {https:\/\/arxiv.org\/abs\/2208.10989},
\r\ndoi = {10.1016\/j.matpur.2023.06.008},
\r\nyear  = {2023},
\r\ndate = {2023-09-01},
\r\nurldate = {2023-04-28},
\r\njournal = {Journal de Math\u00e9matiques Pures et Appliqu\u00e9es},
\r\nvolume = {177},
\r\nnumber = {1},
\r\npages = {45},
\r\nabstract = {Determining the existence of compact invariant manifolds is a central quest in the qualitative theory of differential equations. Singularities, periodic solutions, and invariant tori are examples of such invariant manifolds. A classical and useful result from the averaging theory relates the existence of isolated periodic solutions of non-autonomous periodic differential equations, given in a specific standard form, with the existence of simple singularities of the so-called guiding system, which is an autonomous differential equation given in terms of the average in time of the original non-autonomous one. In this paper, we provide an analogous result for the existence of invariant tori. Namely, we show that a non-autonomous periodic differential equation, given in the standard form, has a normally hyperbolic invariant torus in the extended phase space provided that the guiding system has a hyperbolic limit cycle. We apply this result to show the existence of normally hyperbolic invariant tori in a family of jerk differential equations.},
\r\nkeywords = {},
\r\npubstate = {published},
\r\ntppubtype = {article}
\r\n}
\r\n<\/pre><\/div>
Fechar<\/a><\/p><\/div>
Determining the existence of compact invariant manifolds is a central quest in the qualitative theory of differential equations. Singularities, periodic solutions, and invariant tori are examples of such invariant manifolds. A classical and useful result from the averaging theory relates the existence of isolated periodic solutions of non-autonomous periodic differential equations, given in a specific standard form, with the existence of simple singularities of the so-called guiding system, which is an autonomous differential equation given in terms of the average in time of the original non-autonomous one. In this paper, we provide an analogous result for the existence of invariant tori. Namely, we show that a non-autonomous periodic differential equation, given in the standard form, has a normally hyperbolic invariant torus in the extended phase space provided that the guiding system has a hyperbolic limit cycle. We apply this result to show the existence of normally hyperbolic invariant tori in a family of jerk differential equations.<\/div>
Fechar<\/a><\/p><\/div>