Related papers: Hyperbolicity of minimal periodic orbits
It is proved that a certain type of monotone flow has a global period provided periodic points are dense.
In this paper we give an upper bound of the first eigenvalue of the Laplace operator on a complete stable minimal hypersurface $M$ in the hyperbolic space which has finite $L^2$-norm of the second fundamental form on $M$. We provide some…
Impulsive dynamical systems, modeled by a continuous semiflow and an impulse function, may be discontinuous and may have non-intuitive topological properties, as the non-invariance of the non-wandering set or the non-existence of invariant…
The starting point of this paper is the computation of minimal hyperbolic polynomials of duals of cones arising from chordal sparsity patterns. From that, we investigate the relation between ranks of homogeneous cones and their minimal…
We study ergodic properties of partially hyperbolic systems whose central direction is mostly contracting. Earlier work of Bonatti, Viana about existence and finitude of physical measures is extended to the case of local diffeomorphisms.…
In this article we mainly aim to know what kind of asymptotic behavior of typical orbits can display. For example, we show in any transitive system, the emprical measures of a typical orbit can cover all emprical measures of dense orbits…
In this paper, we prove the nonexistence of $L^2$ harmonic 1-forms on a complete super stable minimal submanifold $M$ in hyperbolic space under the assumption that the first eigenvalue $\lambda_1 (M)$ for the Laplace operator on $M$ is…
We consider in this Note resonances for a $h$-Pseudo-Differential Operator $H(x,hD_x;h)$ on $L^2(M)$ induced by a periodic orbit of hyperbolic type, as arises for Schr\"odinger operator with AC Stark effect when $M={\bf R}^n$, or the…
Compact locally maximal hyperbolic sets are studied via geometrically defined functional spaces that take advantage of the smoothness of the map in a neighborhood of the hyperbolic set. This provides a self-contained theory that not only…
We prove that a compact simply connected manifold $M$ with a variationally complete $G$-action satisfying certain mild conditions (e.g. trivial principal isotropy, or simply connected principal orbits) is rationally elliptic if and only if…
This paper studies a class of $1\frac12$-degree-of-freedom Hamiltonian systems with a slowly varying phase that unfolds a Hamiltonian pitchfork bifurcation. The main result of the paper is that there exists an order of…
We perform a parameter study of non-spinning, equal and unequal mass black hole binaries on generic, eccentric orbits in numerical relativity. The linear momentum considered ranges from that of a circular orbit to ten times that value. We…
Determination of periodic orbits for a Hamiltonian system together with their semi-classical quantization has been a long standing problem. We consider here resonances for a $h$-Pseudo-Differential Operator $H(y,hD_y;h)$ induced by a…
In this text we study billiards on ovals and investigate some consequences of a rotational symmetry of the boundary on the dynamics. As it simplifies some calculations, the symmetry helps to obtain the results. We focus on periodic orbits…
We summarize some characteristic features of the frustrated magnetic interactions in spin-orbital models adequate for cubic transition metal oxides with orbital degeneracy. A generic tendency towards dimerization, found already in the…
We describe some recent results on the dynamics of singular-hyperbolic (or Lorenz-like) attractors: attractors in this class are expansive and so sensitive with respect to initial data; they admit a unique physical measure whose support is…
Quasiperiodic behaviour is known to occur in systems with enforced quasiperiodicity or randomness, in either the lattice structure or the potential, as well as in periodically driven systems. Here, we present instead a setting where…
We develop a gauge-independent perturbation theory for the grand potential of itinerant electrons in two-dimensional tight-binding models in the presence of a perpendicular magnetic field. At first order in the field, we recover the result…
We consider a simple class of fast-slow partially hyperbolic dynamical systems and show that the (properly rescaled) behaviour of the slow variable is very close to a Friedlin--Wentzell type random system for times that are rather long, but…
For a nearly integrable Hamiltonian systems $H=h(p)+\epsilon P(p,q)$ with $(p,q)\in\mathbb{R}^3\times\mathbb{T}^3$, large normally hyperbolic invariant cylinders exist along the whole resonant path, except for the…