Basin of attraction of triangular maps with applications

We consider some planar triangular maps. These maps preserve certain fibration of the plane. We assume that there exists an invariant attracting fiber and we study the limit dynamics of those points in the basin of attraction of this invariant fiber, assuming that either it contains a global attractor, or it is filled by fixed or 2-periodic points. Finally, we apply our results to a variety of examples, from particular cases of triangular systems to some planar quasi-homogeneous maps, and some multiplicative and additive difference equations, as well.Comment: 1 figur

Non-integrability of measure preserving maps via Lie symmetries

We consider the problem of characterizing, for certain natural number $m$, the local $\mathcal{C}^m$-non-integrability near elliptic fixed points of smooth planar measure preserving maps. Our criterion relates this non-integrability with the existence of some Lie Symmetries associated to the maps, together with the study of the finiteness of its periodic points. One of the steps in the proof uses the regularity of the period function on the whole period annulus for non-degenerate centers, question that we believe that is interesting by itself. The obtained criterion can be applied to prove the local non-integrability of the Cohen map and of several rational maps coming from second order difference equations.Comment: 25 page

The haemocytes of the colonial aplousobranch ascidian Diplosoma listerianum: Structural, cytochemical and functional analyses

Diplosoma listerianum is a colonial aplousobranch ascidian of the family Didemnidae that is native to the northeast Atlantic and exhibits a cosmopolitan distribution in temperate waters. It lacks a shared colonial circulation crossing the tunic, and the zooids are connected only by the common tunic. In the present study, the haemocytes of this ascidian were analysed via light and electron microscopy. Their phagocytic and enzymatic activities, staining and immunostaining properties, and lectin affinity were examined with various classical methods reconsidered and modified for small marine invertebrates. Eight morphotypes were identified in reference to corresponding cell types described in other ascidians: undifferentiated cells (haemoblasts), storage cells for nitrogenous catabolites (nephrocytes) and immunocytes. The immunocytes are involved in immune responses, acting as (1) phagocytes, rich in hydrolases and involved in the clearance of both foreign particles and effete cells (hyaline amoebocytes and macrophage-like cells); (2) cytotoxic cells, able to degranulate and induce cytotoxicity through the release of the enzyme phenoloxidase after an immune stimulus (granular amoebocytes and morula cells); and (3) basophilic cells with an affinity for ConA and NPA that contain heparin and histamine and that show sensitivity to the compound 48/80, promoting their degranulation (mast cell-like granulocytes). In addition, a particular cell type showing exceptional development of the Golgi apparatus and large vacuoles containing a filamentous material has been recognised (spherule cell), for which a role in tunic repair and fibrogenesis has been hypothesised

Parrondo's dynamic paradox for the stability of non-hyperbolic fixed points

We show that for periodic non-autonomous discrete dynamical systems, even when a common fixed point for each of the autonomous associated dynamical systems is repeller, this fixed point can became a local attractor for the whole system, giving rise to a Parrondo's dynamic type paradox.Comment: 21 page

Studying discrete dynamical systems trough differential equations

In this paper we consider dynamical systems generated by a diffeomorphism F defined on U an open subset of R^n, and give conditions over F which imply that their dynamics can be understood by studying the flow of an associated differential equation, $\dot x=X(x),$ also defined on U. In particular the case where F has n-1 functionally independent first integrals is considered. In this case X is constructed by imposing that it shares with $F$ the same set of first integrals and that the functional equation $\mu(F(x))=\det((DF(x))\mu(x),$ for x in U has some non-zero solution. Several examples for n=2,3 are presented, most of them coming from several well-known difference equations.Comment: 22 pages; 3 Figure

Periodic orbits in complex Abel equations

AbstractThis paper is devoted to prove two unexpected properties of the Abel equation dz/dt=z3+B(t)z2+C(t)z, where B and C are smooth, 2π-periodic complex valuated functions, t∈R and z∈C. The first one is that there is no upper bound for its number of isolated 2π-periodic solutions. In contrast, recall that if the functions B and C are real valuated then the number of complex 2π-periodic solutions is at most three. The second property is that there are examples of the above equation with B and C being low degree trigonometric polynomials such that the center variety is formed by infinitely many connected components in the space of coefficients of B and C. This result is also in contrast with the characterization of the center variety for the examples of Abel equations dz/dt=A(t)z3+B(t)z2 studied in the literature, where the center variety is located in a finite number of connected components

Konstrukce „já“ v povídce „Strana“ autorky Kurahaši Jumiko

The Japanese writer Kurahashi Yumiko 倉橋由美子 (1935–2005) debuted in 1960 with a short story “Party” (Parutai パルタイ), in which the narrator, a young student, writes about her relationship to a young member of a leftist party and to the party itself. This article examines what motifs Kurahasi Yumiko uses to construct the “self ” of the narrator, how this “self ” changes and evolves in relation to other characters and to the party, and what the final escape from the net of interpersonal-political relations means for the narrator

Pointwise periodic maps with quantized first integrals

In this paper we describe the global dynamics of some interesting pointwise periodic piecewise linear maps in the plane. For each of these maps we find a first integral. These first integrals exhibit unusual characteristics which are quite novel in the context of discrete dynamical systems theory: for instance, the set of values of the integrals are discrete, thus quantized. Furthermore, the level sets are bounded sets whose interior is formed by a finite number of open tiles of certain regular tessellations. The action of the maps on each invariant set of tiles is then described geometrically.Comment: 43 pages, 21 figure