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This paper combines the decay of high modes with the smallness introduced by high orders, leading to a normal form lemma for infinite-dimensional Hamiltonian systems under ultra-differentiable regularity. We prove the sub-exponential…
We present an alternative account of the problem of classifying and finding normal forms for arbitrary bilinear forms. Beginning from basic results developed by Riehm, our solution to this problem hinges on the classification of…
We revisit the dynamics of the post-Newtonian (PN) two-body problem for two inspiraling compact bodies. Starting from a matter-only reduced Hamiltonian, we present an adapted framework based on the Lie series approach, enabling the…
It is shown that the presence of Lie-point-symmetries of (non-Hamiltonian) dynamical systems can ensure the convergence of the coordinate transformations which take the dynamical sytem (or vector field) into Poincar\'e-Dulac normal form.
The problem of stability of the triangular libration points in the planar circular restricted three-body problem is considered. A software package, intended for normalization of autonomous Hamiltonian systems by means of computer algebra,…
We sketch out a new geometric framework to construct Hamiltonian operators for generic, non-evolutionary partial differential equations. Examples on how the formalism works are provided for the KdV equation, Camassa-Holm equation, and…
The equilibrium configuration of an engineering structure, able to withstand a certain loading condition, is usually associated with a local minimum of the underlying potential energy. However, in the nonlinear context, there may be other…
We present a normal form for travelling waves in one-dimensional excitable media in form of a differential delay equation. The normal form is built around the well-known saddle-node bifurcation generically present in excitable media. Finite…
The theory of bi-orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to…
We consider a class of two-degree-of-freedom Hamiltonian systems with saddle-centers connected by heteroclinic orbits and discuss some relationships between the existence of transverse heteroclinic orbits and nonintegrability. By the…
We show that, in addition to SO(4), the Hubbard model at half filling on a bipartite lattice has a group of discrete symmetries and transformations. A unique Hubbard-Stratonovich decomposition of the interaction term, incorporating both…
For a field $E$ of characteristic different from $2$ and cohomological $2$-dimension one, quadratic forms over the rational function field $E(X)$ are studied. A characterisation in terms of polynomials in $E[X]$ is obtained for having that…
The aim of this paper is to obtain polynomial decay of correlations of a Lorenz-like flow where the hyperbolic saddle at the origin is replaced by a neutral saddle. To do that, we take the construction of the geometrical Lorenz flow and…
In this work, we study the motions in the region around the equilateral Lagrangian equilibrium points L4 and L5, in the framework of the Circular Planar Restricted Three-Body Problem (hereafter, CPRTBP). We design a semi-analytic approach…
In earlier works on Shape Dynamics (SD), a linear method of solving a particular set of Lichnerowicz-type equations through the implicit function theorem was developed in order to implicitly construct SD's global Hamiltonian and eliminate…
We focus on the existence and persistence of families of saddle periodic orbits in a four-dimensional Hamiltonian reversible ordinary differential equation derived using a travelling wave ansatz from a generalised nonlinear Schr{\"o}dinger…
We study the existence and instability properties of saddle-shaped solutions of the semilinear elliptic equation $-\Delta u = f(u)$ in the whole $\R^{2m}$, where $f$ is of bistable type. It is known that in dimension $2m=2$ there exists a…
Saddle-node bifurcations arise frequently in solitary waves of diverse physical systems. Previously it was believed that solitary waves always undergo stability switching at saddle-node bifurcations, just as in finite-dimensional dynamical…
We show that complex Langevin simulation converges to a wrong result, by relating it to the Lefschetz-thimble path integral, when the path-integral weight has different phases among dominant complex saddle points. Equilibrium solution of…
In this work we consider formal singular vector fields in $ C^{3}$with an isolated and doubly-resonant singularity of saddle-node typeat the origin. Such vector fields come from irregular two-dimensionalsystems with two opposite non-zero…