‎In this work‎, ‎we investigate admitting center map on multiplicative metric space‎ ‎and establish some fixed point theorems for such maps‎. ‎We modify the Banach contraction principle and‎ ‎the Caristi's fixed point theorem for M-contraction admitting center maps and we prove some‎ ‎useful theorems‎. ‎Our results on multiplicative metric space improve and modify‎ ‎s...

In this work we investigate a class of admitting center maps on a metric space. We state and prove some fixed point and best proximity point theorems for them. We obtain some results and relevant examples. In particular, we show that if $X$ is a reflexive Banach space with the Opial condition and $T:Crightarrow X$ is a continuous admiting center map, then $T$ has a fixed point in $X.$ Also, we ...

Abst ract A homoclinic orbit is considered for which the center-stable and center-unstable manifolds of a saddle-node equilibrium have a quadratic tangency. This bifurcation is of codimension two and leads generically to the creation of a bifurcation curve deening two independent transverse homoclinic orbits to a saddle-node. This latter case was shown by L.P. Shilnikov to imply shift dynamics....

The goal of this article is to establish several general properties a somewhat large class partially hyperbolic diffeomorphisms called discretized Anosov flows. A definition for these systems presented and proven be equivalent with the introduced in [1], as well notion flow type [13].The set flows shown $ C^1 $-open closed inside diffeomorphisms. Every dynamically coherent plaque expansive. Uni...

A few years ago, the first example of a closed manifold admitting an Anosov diffeomorphism but no expanding map was given. Unfortunately, this is not explicit and high-dimensional, although its exact dimension unknown due to type construction. In paper, we present family concrete 12-dimensional nilmanifolds with map, where nilmanifold defined as quotient 1-connected nilpotent Lie group by cocom...

We compute the rational Chow class of the locus of genus 2 curves admitting a d-to-1 map to a genus 1 curve, recovering a result of Faber-Pagani when d = 2. As an application, we compute the number of d-elliptic curves in a very general family of genus 2 curves obtained by fixing five branch points of the hyperelliptic map and varying the sixth.