Related papers: Heteroclinic connections between finite-amplitude …
Focusing on a two-field Swift-Hohenberg model with linear nonreciprocal interactions, this study investigates how emerging higher-codimension points act as organizing centers for the nonequilibrium phase diagram that features various steady…
The analysis performed as well as extensive numerical simulations have revealed the possibility of the generation of homoclinic orbits as a result of homoclinic bifurcation in a porous pellet. A method has been proposed for the development…
In this paper we consider a semilinear parabolic equation in an infinite cylinder. The spatially varying nonlinearity is such that it connects two (spatially independent) bistable nonlinearities in a compact set in space. We prove that,…
The two-dimensional Heisenberg spin-glass model is investigated by means of a semiclassical expansion around classical states. At leading order, we obtain an effective quadratic spin-wave Hamiltonian and study the localization properties of…
We construct heteroclinic orbits for a strongly nonlocal integro-differential equation. Since the energy associated to the equation is infinite in such strongly nonlocal regime, the proof, based on variational methods, relies on a…
In this paper we study a beyond all order phenomenon which appears in the analytic unfoldings of the Hopf-zero singularity. It consists in the breakdown of a two-dimensional heteroclinic surface which exists in the truncated normal form of…
This paper presents methodology for the computation of whole sets of heteroclinic connections between iso-energetic slices of center manifolds of center x center x saddle fixed points of autonomous Hamiltonian systems. It involves: (a)…
We present an extension of the theory known as Lin's method to heteroclinic chains that connect hyperbolic equilibria and hyperbolic periodic orbits. Based on the construction of a so-called Lin orbit, that is, a sequence of continuous…
In this paper we present a computer-assisted procedure for proving the existence of transverse heteroclinic orbits connecting hyperbolic equilibria of polynomial vector fields. The idea is to compute high-order Taylor approximations of…
In a 2D conservative Hamiltonian system there is a formal integral $\Phi$ besides the energy H. This is not convergent near a stable periodic orbit, but it is convergent near an unstable periodic orbit. We explain this difference and we…
Using a vector field in $\mathbb{R}^4$, we provide an example of a robust heteroclinic cycle between two equilibria that displays a mix of features exhibited by well-known types of low-dimensional heteroclinic structures, including simple,…
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…
We establish a necessary and sufficient condition for the birth of heterodimensional cycles from a generic homoclinic tangency to a hyperbolic periodic orbit. We prove for $C^r$ ($r=3,\dots,\infty,\omega$) dynamical systems on a manifold…
We prove a general theorem on the existence of heteroclinic orbits in Hilbert spaces, and present a method to reduce the solutions of some P.D.E. problems to such orbits. In our first application, we give a new proof in a slightly more…
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 investigate the evolution of families of periodic orbits in a bisymmetrical potential made up of a two-dimensional harmonic oscillator with only one quartic perturbing term, in a number of resonant cases. Our main objective is to compute…
This paper investigates the dynamics of a particle orbiting around a rotating homogeneous cube, and shows fruitful results that have implications for examining the dynamics of orbits around non-spherical celestial bodies. This study can be…
Heteroclinic-induced spiral waves may arise in systems of partial differential equations that exhibit robust heteroclinic cycles between spatially uniform equilibria. Robust heteroclinic cycles arise naturally in systems with invariant…
We study the continuation of periodic orbits from various compound of homoclinics in classical system. Together with the homoclinics, the periodic orbits make up a $C^1$-smooth, normally hyperbolic invariant cylinder with holes. It plays a…
Existence of homoclinic orbits in the cubic nonlinear Schr\"odinger equation under singular perturbations is proved. Emphasis is placed upon the regularity of the semigroup $e^{\e t \pa_x^2}$ at $\e = 0$. This article is a substantial…