Displaying similar documents to “A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: announcement of results.”

Optimal stability and instability results for a class of nearly integrable Hamiltonian systems

Massimiliano Berti, Luca Biasco, Philippe Bolle (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

We consider nearly integrable, non-isochronous, a-priori unstable Hamiltonian systems with a (trigonometric polynomial) O ⁢ µ -perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with diffusion time T d = O ⁢ 1 / μ ⁢ log ⁡ 1 / μ by a variational method which does not require the existence of «transition chains of tori» provided by KAM theory. We also prove that our estimate of the diffusion time T d is optimal as a consequence of a general stability result proved via classical...

Diffusion time and splitting of separatrices for nearly integrable isochronous Hamiltonian systems

Massimiliano Berti, Philippe Bolle (2000)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

We consider the problem of Arnold’s diffusion for nearly integrable isochronous Hamiltonian systems. We prove a shadowing theorem which improves the known estimates for the diffusion time. We also justify for three time scales systems that the splitting of the separatrices is correctly predicted by the Poincaré-Melnikov function.

A simple proof of the non-integrability of the first and the second Painlevé equations

Henryk Żołądek (2011)

Banach Center Publications

Similarity:

The first and the second Painlevé equations are explicitly Hamiltonian with time dependent Hamilton function. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems in ℂ⁴. We prove that the latter systems do not have any additional algebraic first integral. In the proof equations in variations with respect to a parameter are used.

On the Edge-Hyper-Hamiltonian Laceability of Balanced Hypercubes

Jianxiang Cao, Minyong Shi, Lihua Feng (2016)

Discussiones Mathematicae Graph Theory

Similarity:

The balanced hypercube BHn, defined by Wu and Huang, is a variant of the hypercube network Qn, and has been proved to have better properties than Qn with the same number of links and processors. For a bipartite graph G = (V0 ∪ V1,E), we say G is edge-hyper-Hamiltonian laceable if it is Hamiltonian laceable, and for any vertex v ∈ Vi, i ∈ {0, 1}, any edge e ∈ E(G − v), there is a Hamiltonian path containing e in G − v between any two vertices of V1−i. In this paper, we prove that BHn...

Improved Sufficient Conditions for Hamiltonian Properties

Jens-P. Bode, Anika Fricke, Arnfried Kemnitz (2015)

Discussiones Mathematicae Graph Theory

Similarity:

In 1980 Bondy [2] proved that a (k+s)-connected graph of order n ≥ 3 is traceable (s = −1) or Hamiltonian (s = 0) or Hamiltonian-connected (s = 1) if the degree sum of every set of k+1 pairwise nonadjacent vertices is at least ((k+1)(n+s−1)+1)/2. It is shown in [1] that one can allow exceptional (k+ 1)-sets violating this condition and still implying the considered Hamiltonian property. In this note we generalize this result for s = −1 and s = 0 and graphs that fulfill a certain connectivity...