We consider the infinite-dimensional vector of frequencies, arising from a linear Klein – Gordon equation on the one-dimensional torus and prove that there exists a positive measure set of masses s for which satisfies a Diophantine condition similar to the one introduced by Bourgain in [14],in the context of the Schrödinger equation with convolution potential.The main difficulties we have to deal with arethe asymptotically linear nature of the (infinitely many) s and the degeneracy coming from having only one parameter at disposal for their modulation.As an application we provide estimates on the inverse of the adjoint action of the associated quadratic Hamiltonian on homogenenous polynomials of any degree in Gevrey category.
Feola, R., Massetti, J.E. (2024). Non-Resonant Conditions for the Klein – Gordon Equation on the Circle. REGULAR & CHAOTIC DYNAMICS, 29(4), 541-564 [10.1134/S1560354724040026].
Non-Resonant Conditions for the Klein – Gordon Equation on the Circle
Feola R.
;Massetti J. E.
2024-01-01
Abstract
We consider the infinite-dimensional vector of frequencies, arising from a linear Klein – Gordon equation on the one-dimensional torus and prove that there exists a positive measure set of masses s for which satisfies a Diophantine condition similar to the one introduced by Bourgain in [14],in the context of the Schrödinger equation with convolution potential.The main difficulties we have to deal with arethe asymptotically linear nature of the (infinitely many) s and the degeneracy coming from having only one parameter at disposal for their modulation.As an application we provide estimates on the inverse of the adjoint action of the associated quadratic Hamiltonian on homogenenous polynomials of any degree in Gevrey category.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
