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On the growth of the number of non-compact heteroclinic curves

TitleOn the growth of the number of non-compact heteroclinic curves
AuthorsV. Grines1, E. Gurevich1, O. Pochinka1, A. Shilovskaya2
1National Research University Higher School of Economics
2Lobachevskii State University
AnnotationWe consider a class SD(M3) of gradient-like diffeomorphisms on closed 3-manifolds M3 that have surface dynamics. In~\cite{GrGuPo-rhd} it was proven that the ambient manifold M3 for such diffeomorphisms is a mapping torus Mg,τ, g0, and the number of non-compact heteroclinic curves is no less than 12g. In this paper it is established that for any integer n12g there exists a mapping torus Mg,τ(n) and a diffeomorphism from the class SD(Mg,τ(n)) having exactly n heteroclinic curves.
KeywordsHeteroclinic curve, gradient-like diffeomorphism, mapping torus
CitationGrines V., Gurevich E., Pochinka O., Shilovskaya A. ''On the growth of the number of non-compact heteroclinic curves'' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 398-402. Available at: https://conf.svmo.ru/files/deamm2017/papers/paper56.pdf. - Date of access: 08.04.2025.