相关论文: Entire Parabolic Trajectories as Minimal Phase Tra…

We continue the variational approach to parabolic trajectories introduced in our previous paper [5], which sees parabolic orbits as minimal phase transitions. We deepen and complete the analysis in the planar case for homogeneous singular…

We establish an equivalence between infinitely many asymptotically stable periodic solutions and subsumed homoclinic connections for $N$-dimensional piecewise-linear continuous maps. These features arise as a codimension-three phenomenon.…

We are concerned with the analysis of finite time collision trajectories for a class of singular anisotropic homogeneous potentials of degree $-\alpha$, with $\alpha\in(0,2)$ and their lower order perturbations. It is well known that, under…

We consider the $N$-body problem in $\mathbb{R}^d$ with the newtonian potential $1/r$. We prove that for every initial configuration $x_i$ and for every minimizing normalized central configuration $x_0$, there exists a collision-free…

We study linearization models for continuous one-parameter semigroups of parabolic type. In particular, we introduce new limit schemes to obtain solutions of Abel's functional equation and to study asymptotic behavior of such semigroups.…

Let $F$ be a lower semicontinuous, 1-homogeneous positive function defined on $\mathbf{R}^n$. We provide a characterization of absolutely continuous paths that minimize the anisotropic $F$-length between two points. The characterization is…

The critical behaviour of directed self-avoiding walks is studied on parabolic-like systems with a free boundary at x=\pm Ct^\alpha. Using a scaling argument, 1/C is shown to be a marginal variable when \alpha=\nu_\perp/\nu_\parallel=1/2,…

Periodic and quasi-periodic orbits of the $n$-body problem are critical points of the action functional constrained to the Sobolev space of symmetric loops. Variational methods yield collisionless orbits provided the group of symmetries…

We deal with a class of semilinear parabolic PDEs on the space of continuous functions that arise, for example, as Kolmogorov equations associated to the infinite-dimensional lifting of path-dependent SDEs. We investigate existence of…

We investigate expansive solutions of the $N$-body problem in $\mathbb{R}^d$ ($d\ge2$) driven by homogeneous Newtonian potentials of degree $-\alpha$. We establish the existence of half-entire expansive motions with prescribed initial…

Chaotic attractors commonly contain periodic solutions with unstable manifolds of different dimensions. This allows for a zoo of dynamical phenomena not possible for hyperbolic attractors. The purpose of this Letter is to demonstrate these…

The paper gives a comprehensive study of Inertial Manifolds for hyperbolic relaxations of an abstract semilinear parabolic equation in a Hilbert space. A new scheme of constructing Inertial Manifolds for such type of problems is suggested…

We investigate saddle point configurations in spherical ferromagnets with perpendicular anisotropy. These are modeled by a micromagnetic energy functional on the unit sphere that leads to the emergence of the so-called curvature induced…

We study the motion of a particle in the hyperbolic plane (embedded in Minkowski space), under the action of a potential that depends only on one variable. This problem is the analogous to the spherical pendulum in a unidirectional force…

In this paper we study the phenomenon of phase transitions for the geodesic flow on some geometrically finite negatively curved manifolds. We define a class of potentials going slowly to zero through the cusps of $M$ for which the pressure…

We establish sufficient conditions for existence of curves minimizing length as measured with respect to a degenerate metric on the plane while enclosing a specified amount of Euclidean area. Non-existence of minimizers can occur and…

A wide variety of intricate dynamics may be created at border-collision bifurcations of piecewise-smooth maps, where a fixed point collides with a surface at which the map is nonsmooth. For the border-collision normal form in two…

The work is devoted to the construction of the asymptotic behavior of the solution of a singularly perturbed system of equations of parabolic type, in the case when the limit equation has a regular singularity as the small parameter tends…

As a starting point of our research, we show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to…

The border-collision normal form is a piecewise-linear continuous map on $\mathbb{R}^N$ that describes dynamics near border-collision bifurcations of nonsmooth maps. This paper studies a codimension-three scenario at which the…