Fixed points of log-linear discrete dynamics.
Fixed points, periodic points, and coin-tossing sequences for mappings defined on two-dimensional cells.
Flow equivalence, hyperbolic systems and a new zeta function for flows.
Generic properties of the rotation number of one-parameter diffeomorphisms of the circle
Generic robustness of spectral decompositions
Géométrie des variétés invariantes d'un difféomorphisme axiome A et transversalité forte
Gyration numbers for involutions of subshifts of finite type II.
Gyration numbers for involutions of subshifts of finite type I.
Invariants of twist-wise flow equivalence.
Jordan tori and polynomial endomorphisms in
For a class of quadratic polynomial endomorphisms close to the standard torus map , we show that the Julia set J(f) is homeomorphic to the torus. We identify J(f) as the closure ℛ of the set of repelling periodic points and as the Shilov boundary of the set K(f) of points with bounded forward orbit. Moreover, it turns out that (J(f),f) is a mixing repeller and supports a measure of maximal entropy for f which is uniquely determined as the harmonic measure for K(f).
Krasnoselskii-type fixed point theorems under weak topology settings and applications.
Large deviation asymptotics for Anosov flows
Large deviations, Gibbs measures and closed orbits for hyperbolic flows.
Minimal number of periodic points for smooth self-maps of S³
Let f be a continuous self-map of a smooth compact connected and simply-connected manifold of dimension m ≥ 3 and r a fixed natural number. A topological invariant , introduced by the authors [Forum Math. 21 (2009)], is equal to the minimal number of r-periodic points for all smooth maps homotopic to f. In this paper we calculate for all self-maps of S³.
Minimal periods of maps of rational exterior spaces
The problem of description of the set Per(f) of all minimal periods of a self-map f:X → X is studied. If X is a rational exterior space (e.g. a compact Lie group) then there exists a description of the set of minimal periods analogous to that for a torus map given by Jiang and Llibre. Our approach is based on the Haibao formula for the Lefschetz number of a self-map of a rational exterior space.
Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers
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...
Multimodal cycles with linear map having exactly one fixed point.
Nielsen fixed point theory and symplectic Floer homology
We describe a connection between Nielsen fixed point theory and symplectic Floer homology for surfaces. A new asymptotic invariant of symplectic origin is defined.
Nielsen number is a knot invariant
We show that the Nielsen number is a knot invariant via representation variety.
Non-accessible critical points of certain rational functions with Cremer points.