Bifurcations in the Lozi map

We study the presence in the Lozi map of a type of abrupt order-to-order and order-to-chaos transitions which are mediated by an attractor made of a continuum of neutrally stable limit cycles, all with the same period.Comment: 17 pages, 12 figure

An extension of the Artin-Mazur theorem

Let M be a compact manifold. We call a mapping f in C^r(M,M) an Artin-Mazur mapping if the number of isolated periodic points of f^n grows at most exponentially in n. Artin and Mazur posed the following problem: What can be said about the set of Artin-Mazur mappings with only transversal periodic orbits? Recall that a periodic orbit of period n is called transversal if the linearization df^n at this point has for an eigenvalue no nth roots of unity. Notice that a hyperbolic periodic point is always transversal, but not vice versa. We consider not the whole space C^r(M,M) of mappings of M into itself, but only its open subset Diff^r(M). The main result of this paper is the following theorem: Let 1 <= r < \infty. Then the set of Artin-Mazur diffeomorphisms with only hyperbolic periodic orbits is dense in the space Diff^r(M).Comment: 13 pages, published version, abstract added in migratio

Bifurcation from relative periodic solutions

Published versio