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Izvestiya: Mathematics, 2020, Volume 84, Issue 1, Pages 23–51
DOI: https://doi.org/10.1070/IM8786 (Mi im8786) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On mixed dynamics of two-dimensional reversible diffeomorphisms with symmetric non-transversal heteroclinic cycles

S. V. Gonchenkoa, M. S. Gonchenkob, I. O. Sinitskya

a Lobachevski State University of Nizhni Novgorod
b Universitat Politecnica de Catalunya, Barcelona, Spain
English version PDF (837 kB) Citations (5)
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DOI: https://doi.org/10.1070/IM8786
Abstract: We consider one-parameter families (general unfoldings) of two-dimensional reversible diffeomorphisms that contain a diffeomorphism with a symmetric non-transversal heteroclinic cycle. We show that in such families there exist Newhouse intervals of parameters such that the values corresponding to the co-existence of infinitely many stable, completely unstable, saddle and symmetric elliptic periodic orbits are generic (that is, they form Baire second-category sets). Also, the closures of the sets of orbits of different types have non-empty intersections.
Keywords: heteroclinic cycle, reversible diffeomorphism, homoclinic tangency, bifurcation, periodic orbit, mixed dynamics.
Funding agency Grant number
Russian Science Foundation 19-11-00280
Russian Foundation for Basic Research 19-01-00607
18-29-10081
Ministry of Science and Higher Education of the Russian Federation 1.3287.2017
Ministerio de Ciencia e Innovación de España FJCI-2014-21229
IJCI-2016-29071
MTM2015-65715-P
Ministerio de Economía y Competitividad de España MTM2016-80117-P
PGC2018-098676-B-I00
Generalitat de Catalunya 2017SGR1374
This work was supported the Russian Science Foundation (grant no. 19-11-00280). S. Gonchenko and I. Sinitsky thank the Russian Foundation for Basic Research (grants no. 19-01-00607 and no. 18-29-10081) and the Russian Ministry of Science and Education (project 1.3287.2017, target part) for their support of scientific research. M. Gonchenko was partially supported by the Spanish grants Juan de la Cierva-Formación FJCI-2014-21229, Juan de la Cierva-Incorporación IJCI-2016-29071, MICIIN/FEDER MTM2015-65715-P, MTM2016-80117-P (MINECO/FEDER, UE), PGC2018-098676-B-I00 (AEI/FEDER/UE) and 2017SGR1374.
Received: 20.03.2018
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2020, Volume 84, Issue 1, Pages 27–59
DOI: https://doi.org/10.4213/im8786
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: Primary 37C05; Secondary 34C15, 34C37
Language: English
Original paper language: Russian
Citation: S. V. Gonchenko, M. S. Gonchenko, I. O. Sinitsky, “On mixed dynamics of two-dimensional reversible diffeomorphisms with symmetric non-transversal heteroclinic cycles”, Izv. RAN. Ser. Mat., 84:1 (2020), 27–59; Izv. Math., 84:1 (2020), 23–51
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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