Related papers: Closed orbits and their bifurcations in the crosse…
We study bifurcations of area-preserving maps, both orientable (symplectic) and non-orientable, with quadratic homoclinic tangencies. We consider one and two parameter general unfoldings and establish results related to the appearance of…
We describe a new mechanism that triggers periodic orbits in smooth dynamical systems. To this end, we introduce the concept of hybrid bifurcations: Such bifurcations occur when a line of equilibria with an exchange point of normal…
This paper deals with periodic solutions of the Hamilton equation with many parameters. Theorems on global bifurcation of solutions with periods $2\pi/j,$ $j\in\mathbb{N},$ from a stationary point are proved. The Hessian matrix of the…
We implement the geometric method proposed in ([9], [3], [16]) to analytically predict the sequence of bifurcations leading to a change of stability and/or the appearance of new periodic orbits in the secular 3D planetary three body…
We study local bifurcations of periodic solutions to time-periodic (systems of) integrodifference equations over compact habitats. Such infinite-dimensional discrete dynamical systems arise in theoretical ecology as models to describe the…
We study generalization of median triangles on the plane with two complex parameters. By specialization of the parameters, we produce periodical motion of a triangle whose vertices trace each other on a common closed orbit.
We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under…
We have derived a semiclassical trace formula for the level density of the three-dimensional spheroidal cavity. To overcome the divergences occurring at bifurcations and in the spherical limit, the trace integrals over the action-angle…
The semiclassical origins of the enhancement of shell effects in exotic-shape mean-field potentials are investigated by focusing attention on the roles of the local symmetries associated with the periodic-orbit bifurcations. The deformed…
We study how the singular behaviour of classical systems at bifurcations is reflected by their quantum counterpart. The semiclassical contributions of individual periodic orbits to trace formulae of Gutzwiller type are known to diverge when…
In the present work, metrics which lead to projected closed orbits are found by comparing the relativistic differential equation of orbits with the corresponding classical differential equation. Physical and geometrical properties of these…
Singular Hopf bifurcation occurs in generic families of vector-fields with two slow variables and one fast variable. Normal forms for this bifurcation depend upon several parameters, and the dynamics displayed by the normal forms is…
We study local biholomorphisms with finite orbits in some neighborhood of the origin since they are intimately related to holomorphic foliations with closed leaves. We describe the structure of the set of periodic points in dimension 2. As…
Given two elements of a vector space acted on by a reductive group, we ask whether they lie in the same orbit, and if not, whether one lies in the orbit closure of the other. We develop techniques to optimize the orbit and orbit closure…
The rational cohomology of a coadjoint orbit ${\cal O}$ is expressed as tensor product of the cohomology of other coadjoint orbits ${\cal O}_k$, with $ \hbox{dim} {\cal O}_k< \hbox{dim} {\cal O}$.
In this work we consider a general class of $2$-dimensional hybrid systems. Assuming that the system possesses an attracting equilibrium point, we show that, when periodically driven with a square-wave pulse, the system possesses a periodic…
We study bifurcations of cubic homoclinic tangencies in two-dimensional symplectic maps. We distinguish two types of cubic homoclinic tangencies, and each type gives different first return maps derived to diverse conservative cubic H\'enon…
Although hydrogen in external fields is a paradigm for the application of periodic orbits and the Gutzwiller trace formula to a real system, the trace formula has never been applied successfully to other Rydberg atoms. We show that spectral…
Analytical perturbations of a family of finite-dimensional Poisson systems are considered. It is shown that the family is analytically orbitally conjugate in $U \subset \mathbb{R}^n$ to a planar harmonic oscillator defined on the symplectic…
We consider a compact manifold of dimension greater than 2 and a differential form of degree one which is closed but non-exact. This form, viewed as a multi-valued function has a gradient vector field with respect to any Riemannian metric.…