Closed orbits of -extension of ergodic toral automorphisms.
Complex Oscillations and Limit Cycles in Autonomous Two-Component Incommensurate Fractional Dynamical Systems
MSC 2010: 26A33, 34D05, 37C25In the paper, long-time behavior of solutions of autonomous two-component incommensurate fractional dynamical systems with derivatives in the Caputo sense is investigated. It is shown that both the characteristic times of the systems and the orders of fractional derivatives play an important role for the instability conditions and system dynamics. For these systems, stationary solutions can be unstable for wider range of parameters compared to ones in the systems with...
Contractions of Nadler type on partial tvs-cone metric spaces
This paper introduces partial tvs-cone metric spaces as a common generalization of both tvs-cone metric spaces and partial metric spaces, and gives a new fixed point theorem for contractions of Nadler type on partial tvs-cone metric spaces. As corollaries, we obtain the main results of S. B. Nadler (1969), D. Wardowski (2011), S. Radenović et al. (2011) and H. Aydi et al. (2012) are deduced.
Countable contraction mappings in metric spaces: invariant sets and measure
We consider a complete metric space (X, d) and a countable number of contraction mappings on X, F = {F i: i ∈ ℕ}. We show the existence of a smallest invariant set (with respect to inclusion) for F. If the maps F i are of the form F i(x) = r i x + b i on X = ℝd, we prove a converse of the classic result on contraction mappings, more precisely, there exists a unique bounded invariant set if and only if r = supi r i is strictly smaller than 1. Further, if ρ = {ρ k}k∈ℕ is a probability sequence, we...
Counting periodic points of -adic power series
Cycles of polynomials in algebraically closed fields of positive characteristic
Cycles of polynomials in algebraically closed fields of positive characteristic (II)
Décomposition des difféomorphismes du tore en applications déviant la verticale (avec un appendice en collaboration avec Jean-Marc Gambaudo)
Disques de Siegel et anneaux de Herman
Distortion bounds for unimodal maps
We obtain estimates for derivative and cross-ratio distortion for (any η > 0) unimodal maps with non-flat critical points. We do not require any “Schwarzian-like” condition. For two intervals J ⊂ T, the cross-ratio is defined as the value B(T,J): = (|T| |J|)/(|L| |R|) where L,R are the left and right connected components of T∖J respectively. For an interval map g such that is a diffeomorphism, we consider the cross-ratio distortion to be B(g,T,J): = B(g(T),g(J))/B(T,J). We prove that for...
Dynamics in binary neural networks with a finite number of patterns. I: General picture of the asynchronous zero temperature dynamics.
Dynamics of the continued fraction map and the spectral theory of SL (2, Z).
Dynamics of the radix expansion map.
Dynamique des homéomorphismes du plan au voisinage d'un point fixe
Eventually periodic points of infra-nil endomorphisms.
Existence criterions for generalized solutions of functional boundary value problems without growth restrictions
Expanding attractors
Factorisation of Lefschetz zeta functions and twisted periodic orbits.
Factors and Extensions of Full Shifts.
Fixed points of discrete nilpotent group actions on
We prove that for each integer there is an open neighborhood of the identity map of the 2-sphere , in topology such that: if is a nilpotent subgroup of with length of nilpotency, generated by elements in , then the natural -action on has nonempty fixed point set. Moreover, the -action has at least two fixed points if the action has a finite nontrivial orbit.