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Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers

100%

Graff G., Kaczkowska A.

Open Mathematics

2012

tom 10

nr 6

2160-2172

Let f be a smooth self-map of m-dimensional, m ≥ 4, smooth closed connected and simply-connected 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 self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers, Ann. Polon. Math. (in press)] the topological invariant J[f] which is equal to the minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of f. In this paper the invariant J[f] is computed for self-maps of 4-manifold M with dimH 2(M; ℚ) ≤ 4 and estimated for other types of manifolds. We also use J[f] to compare minimization of the number of periodic points in smooth and in continuous categories.

Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics

63%

Bandman T., Garion S., Kunyavskiĭ B.

Open Mathematics

2014

tom 12

nr 2

175-211

We present a survey of results on word equations in simple groups, as well as their analogues and generalizations, which were obtained over the past decade using various methods: group-theoretic and coming from algebraic and arithmetic geometry, number theory, dynamical systems and computer algebra. Our focus is on interrelations of these machineries which led to numerous spectacular achievements, including solutions of several long-standing problems.

Ograniczanie wyników

2 Open Mathematics

1 Bandman T.

1 Garion S.

1 Graff G.

1 Kaczkowska A.

1 Kunyavskiĭ B.

1 2014

1 2012

Wyniki wyszukiwania

Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers

Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics