相关论文: KAM tori are no more than sticky

{\bf Abstract}: The existence of 2-dimensional KAM tori is proved for the perturbed generalized nonlinear vibrating string equation with singularities $u_{tt}=((1-x^2)u_x)_x-mu-u^3$ subject to certain boundary conditions by means of…

We give a proof of the convergence of an algorithm for the construction of lower dimensional elliptic tori in nearly integrable Hamiltonian systems. The existence of such invariant tori is proved by leading the Hamiltonian to a suitable…

We prove an infinite dimensional KAM theorem which implies the existence of Cantor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations

Perturbations due to round-off errors in computer modeling are discontinuous and therefore one cannot use results like KAM theory about smooth perturbations of twist maps. We elaborate a special approximation scheme to construct two smooth…

In this note, we briefly discuss how singular KAM Theory - which was worked out in a previous work by L.B. and L.C. for the mechanical case $\frac12 |y|^2+\varepsilon f(x)$ - can be extended to convex real analytic nearly integrable…

There are many interesting dynamical systems in which degenerate invariant tori appear. We give conditions under which these degenerate tori have stable and unstable invariant manifolds, with stable and unstable directions having arbitrary…

We establish a condition for the perturbative stability of zero energy nodal points in the quasi-particle spectrum of superconductors in the presence of coexisting \textit{commensurate} orders. The nodes are found to be stable if the…

In this article we reduce the geometric stability conjecture for the scalar torus rigidity theorem to the conformal case via the Yamabe problem. Then we are able to prove the case where a sequence of Riemannian manifolds is conformal to a…

Two Heegaard Floer knot complexes are called stably equivalent if an acyclic complex can be added to each complex to make them filtered chain homotopy equivalent. Hom showed that if two knots are concordant, then their knot complexes are…

We prove the instability of the Couette flow if the disturbances is less smooth than the Gevrey space of class 2. This shows that this is the critical regularity for this problem since it was proved in [5] that stability and inviscid…

We give a simple proof of Kolmogorov's theorem on the persistence of a quasiperiodic invariant torus in Hamiltonian systems. The theorem is first reduced to a well-posed inversion problem (Herman's normal form) by switching the frequency…

We consider non-isochronous, nearly integrable, a-priori unstable Hamiltonian systems with a (trigonometric polynomial) $O(\mu)$-perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with…

Results on stability of tautological sheaves on Hilbert schemes of points are extended to higher dimensions and transferred to abelian surfaces and to the restriction of tautological sheaves to generalised Kummer varieties. This provides a…

We discuss the stability of the topological invariant of the strongly interacting Weyl semi-metal at finite temperature. We find that if the interactions and temperature of the system are controlled by the holography, the topology is stable…

It is well known that instabilities of nearly integrable Hamiltonian systems occur around resonances. Dynamics near resonances of these systems is well approximated by the associated averaged system, called slow system. Each resonance is…

Suppose that two vector fields on a smooth manifold render some equilibrium point globally asymptotically stable (GAS). We show that there exists a homotopy between the corresponding semiflows such that this point remains GAS along this…

We study the question for which commutative ring spectra $A$ the tensor of a simplicial set $X$ with $A$, $X \otimes A$, is a stable invariant in the sense that it depends only on the homotopy type of $\Sigma X$. We prove several structural…

We consider the classical problem of the construction of invariant tori exploiting suitable Hamiltonian normal forms. This kind of approach can be translated by means of the Lie series method into explicit computational algorithms, which…

The goal of the paper is to develop a systematic approach to the study of (perhaps degenerate) singularities of integrable systems and their structural stability. As the main tool, we use "hidden" system-preserving torus actions near…

The parametric equations of KAM tori for a quasi integrable system, are shown to be one point Schwinger functions of a suitable euclidean quantum field theory on the torus. KAM theorem is equivalent to a ultraviolet stability theorem. A…