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

Title On the growth of the number of non-compact heteroclinic curves V. Grines1, E. Gurevich1, O. Pochinka1, A. Shilovskaya21National Research University Higher School of Economics 2Lobachevskii State University We consider a class $SD(M^3)$ of gradient-like diffeomorphisms on closed 3-manifolds $M^3$ that have surface dynamics. In~\cite{GrGuPo-rhd} it was proven that the ambient manifold $M^3$ for such diffeomorphisms is a mapping torus $M_{g,\tau}$, $g\geq 0$, and the number of non-compact heteroclinic curves is no less than $12g$. In this paper it is established that for any integer $n\geq 12g$ there exists a mapping torus $M_{g,\tau(n)}$ and a diffeomorphism from the class $SD(M_{g,\tau(n)})$ having exactly $n$ heteroclinic curves. Heteroclinic curve, gradient-like diffeomorphism, mapping torus Grines 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: http://conf.svmo.ru/files/deamm2017/papers/paper56.pdf. - Date of access: 12.04.2021.