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A spectral sequence calculating the homology groups of some spaces of maps equivariant under compact group actions is described. For the main example, we calculate the rational homology groups of spaces of even and odd maps $S^m \to S^M$,…
Multi-configurational approaches yield universal wave function parameterizations that can qualitatively well describe electronic structures along reaction pathways. For quantitative results, multi-reference perturbation theory is required…
In this work we consider a two-dimensional piecewise smooth system, defined in two domains separated by the switching manifold $x=0$. We assume that there exists a piecewise-defined continuous Hamiltonian that is a first integral of the…
In this paper, it is shown that non-isomorphic effective linear circle actions yield non-diffeomorphic differential structures on the corresponding orbit spaces.
In this paper we prove the breakdown of an heteroclinic connection in the analytic versal unfoldings of the generic Hopf-Zero singularity in an open set of the parameter space. This heteroclinic orbit appears at any order if one performs…
We give a method to determine relative periodic orbits in point vortex systems: it consists mainly into perform a symplectic reduction on a fixed point submanifold in order to obtain a two-dimensional reduced phase space. The method is…
If a Lie group acts on a manifold freely and properly, pulling back by the quotient map gives an isomorphism between the differential forms on the quotient manifold and the basic differential forms upstairs. We show that this result remains…
The accuracy of reaction energy profiles calculated with multi-configurational electronic structure methods and corrected by multi-reference perturbation theory depends crucially on consistent active orbital spaces selected along the…
We propose a new theory to explain the formation of spiral arms and of all types of outer rings in barred galaxies. We have extended and applied the technique used in celestial mechanics to compute transfer orbits. Thus, our theory is based…
Heteroclinic cycles are widely used in neuroscience in order to mathematically describe different mechanisms of functioning of the brain and nervous system. Heteroclinic cycles and interactions between them can be a source of different…
We give a complete description of the shapes and the behavior of all homoclinic orbits in the Euler problem of two fixed centers.
The relation between fixed point and orbit count sequences is investigated from the point of view of linear mappings on the space of arithmetic functions. Spectral and asymptotic properties are derived and several quantities are explicitly…
In many problems of quantum chaos the calculation of sums of products of periodic orbit contributions is required. A general method of computation of these sums is proposed for generic integrable models where the summation over periodic…
We study homoclinic orbits of the Swift-Hohenberg equation near a Hamiltonian-Hopf bifurcation. It is well known that in this case the normal form of the equation is integrable at all orders. Therefore the difference between the stable and…
We study periodic orbits for area-preserving surface diffeomorphisms, particularly some global properities related to the action function and rotation numbers. We generalize recent works of Machel Hutchings [4], proving the existence of…
Symbolic dynamics for homoclinic orbits in the two-dimensional symmetric map, $x_{n+1}+cx_{n}+x_{n-1}=3x_{n}^3$, is discussed. Above a critical $c^{\ast}$, the system exhibits a fully-developed horse-shoe so that its global behavior is…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
Heteroclinic structures organize global features of dynamical systems. We analyze whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more…
We numerically investigate the orbital dynamics of a two-dimensional galactic model, emphasizing the influence of stable and unstable manifolds on the evolution of orbits. In our analysis we use evaluations of the system's Lagrangian…
We study bifurcations of non-orientable area-preserving maps with quadratic homoclinic tangencies. We study the case when the maps are given on non-orientable two-dimensional surfaces. We consider one and two parameter general unfoldings…