Search results for: NIELSEN NUMBER

Computations of the least number of periodic points of smooth boundarypreserving selfmaps of simplyconnected manifolds
PublicationLet $r$ be an odd natural number, $M$ a compact simplyconnected smooth manifold, $\dim M\geq 4$, such that its boundary $\partial M$ is also simplyconnected. We consider $f$, a $C^1$ selfmaps of $M$, preserving $\partial M$. In [G. Graff and J. Jezierski, Geom. Dedicata 187 (2017), 241258] the smooth Nielsen type periodic number $D_r(f;M,\partial M)$ was defined and proved to be equal to the minimal number of $r$periodic points...

Electrondifusion coefficiens in N2O
PublicationW pracy przedstawiono wyniki pomiarów stosunku współczynników dyfuzji poprzecznych i podłużnych do ruchliwości i prędkość dryfu elektronów jako funkcję zredukowanego pola elektrycznego w N2O. Współczynniki dyfuzji wyznaczono stosując metodę TowsendaHuxleya; prędkość dryfu otrzymano używając techniki BradburyNielsen. Całkowitych i częściowych przekrojów czynnych użyto do obliczenia współczynników metodą numeryczną.

Reducing the number of periodic points in the smooth homotopy class of a selfmap of a simplyconnected manifold with periodic sequence of Lefschetz numbers
PublicationLet f be a smooth selfmap of an mdimensional (m >3) closed connected and simplyconnected manifold such that the sequence of the Lefschetz num bers of its iterations is periodic. For a fixed natural r we wish to minimize, in the smooth homotopy class, the number of periodic points with periods less than or equal to r. The resulting number is given by a topological invariant J[f] which is defned in combinatorial terms and is...

Estimation of the minimal number of periodic points for smooth selfmaps of odd dimensional real projective spaces
PublicationLet f be a smooth selfmap of a closed connected manifold of dimension m⩾3. The authors introduced in [G. Graff, J. Jezierski, Minimizing the number of periodic points for smooth maps. Nonsimply connected case, Topology Appl. 158 (3) (2011) 276290] the topological invariant NJD_r[f], where r is a fixed natural number, which is equal to the minimal number of rperiodic points in the smooth homotopy class of f. In this paper smooth...

Minimization of the number of periodic points for smooth selfmaps of simplyconnected manifolds with periodic sequence of Lefschetz numbers
PublicationLet f be a smooth selfmap of mdimensional, m ≥ 4, smooth closed connected and simplyconnected manifold, r a fixed natural number. For the class of maps with periodic sequence of Lefschetz numbers of iterations the authors introduced in [Graff G., Kaczkowska A., Reducing the number of periodic points in smooth homotopy class of selfmaps of simplyconnected manifolds with periodic sequence of Lefschetz numbers, Ann. Polon. Math....

Combinatorial scheme of finding minimal number of periodic points for smooth selfmaps of simply connected manifolds
PublicationLet M be a closed smooth connected and simply connected manifold of dimension m at least 3, and let r be a fixed natural number. The topological invariant D^m_r [f], defined by the authors in [Forum Math. 21 (2009), 491509], is equal to the minimal number of rperiodic points in the smooth homotopy class of f, a given selfmap of M. In this paper, we present a general combinatorial scheme of computing D^m_r [f] for arbitrary dimension...

Minimal number of periodic points of smooth boundarypreserving selfmaps of simplyconnected manifolds
PublicationLet M be a smooth compact and simplyconnected manifold with simplyconnected boundary ∂M, r be a fixed odd natural number. We consider f, a C1 selfmap of M, preserving ∂M . Under the assumption that the dimension of M is at least 4, we define an invariant Dr(f;M,∂M) that is equal to the minimal number of rperiodic points for all maps preserving ∂M and C1homotopic to f. As an application, we give necessary and sufficient...