1,050 research outputs found
Hopf Bifurcations in a Watt Governor With a Spring
This paper pursues the study carried out by the authors in "Stability and
Hopf bifurcation in a hexagonal governor system", focusing on the codimension
one Hopf bifurcations in the hexagonal Watt governor differential system. Here
are studied the codimension two, three and four Hopf bifurcations and the
pertinent Lyapunov stability coefficients and bifurcation diagrams, ilustrating
the number, types and positions of bifurcating small amplitude periodic orbits,
are determined. As a consequence it is found an open region in the parameter
space where two attracting periodic orbits coexist with an attracting
equilibrium point.Comment: 30 pages and 7 figure
The Minimal Geometric Deformation Approach: a brief introduction
We review the basic elements of the Minimal Geometric Deformation approach in
details. This method has been successfully used to generate brane-world
configurations from general relativistic perfect fluid solutions.Comment: Brief review; minor corrections; references adde
Anisotropic solutions by gravitational decoupling
We investigate the extension of isotropic interior solutions for static
self-gravitating systems to include the effects of anisotropic spherically
symmetric gravitational sources by means of the gravitational decoupling
realised via the minimal geometric deformation approach. In particular, the
matching conditions at the star surface with the outer Schwarzschild space-time
are studied in great details, and we describe how to generate, from a single
physically acceptable isotropic solution, new families of anisotropic solutions
whose physical acceptability is also inherited from their isotropic parent.Comment: 20 pages, 4 figures; references and typos corrected; final version to
match the EPJC versio
A causal Schwarzschild-de Sitter interior solution by gravitational decoupling
We employ the minimal geometric deformation approach to gravitational
decoupling (MGD- decoupling) in order to build an exact anisotropic version of
the Schwarzschild interior solution in a space-time with cosmological constant.
Contrary to the well-known Schwarzschild interior, the matter density in the
new solution is not uniform and possesses subluminal sound speed. It therefore
satisfies all standard physical requirements for a candidate astrophysical
object.Comment: 15 pages, 6 figure
Square-free class sizes in products of groups
We obtain some structural properties of a factorised group , given
that the conjugacy class sizes of certain elements in are not
divisible by , for some prime . The case when is a mutually
permutable product is especially considered
Further considerations on the number of limit cycles of vector fields of the form X(v) = Av + f(v) Bv
AbstractIn Gasull, Llibre, and Sotomayor. (J. Differential Equations, in press) we studied the number of limit cycles of planar vector fields as in the title. The case where the origin is a node with different eigenvalues, which then resisted our analysis, is solved in this paper
Canard Cycles and Poincar\'e Index of Non-Smooth Vector Fields on the Plane
This paper is concerned with closed orbits of non-smooth vector fields on the
plane. For a subclass of non-smooth vector fields we provide necessary and
sufficient conditions for the existence of canard kind solutions. By means of a
regularization we prove that the canard cycles are singular orbits of singular
perturbation problems which are limit periodic sets of a sequence of limit
cycles. Moreover, we generalize the Poincar\'e Index for non-smooth vector
fields.Comment: 20 pages, 25 figure
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