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M. Berti

Publications and source records attributed to M. Berti.

6 recordsLinked to original sources

Beyond {\Lambda}CDM with the SKA Observatory -- I: Probing Gravity on Cosmological Scales

General relativity (GR) is currently the best description of the gravitational interaction at our disposal and is one of the foundations of the concordance cosmological model. For as much as we know that GR is not the final theory of gravitation - we still lack an understanding of its fundamental, quantum nature - it has demonstrated a remarkable success in describing observed phenomena and predicting effects that have later been confirmed by laboratory experiments or astronomical observations. Since gravity is extremely weak compared to the other three fundamental interactions, it has so far been tested with exquisite precision only in the strong-field regime. On the immense scales of the cosmos, on the other hand, the gravitational field is extremely weak and spacetime curvature is almost negligible. But crucially, it is on these scales that we see hints at the need for exotic components, such as dark matter and dark energy. The question of whether they really exist or their presence is but an artefact of the incompleteness of our understanding of gravity on cosmological scales then naturally arises. It is therefore paramount to test the validity of GR on these scales, either to further confirm its robustness or to detect deviations that could lead us to the formulation of a more general and conclusive theory of gravitation. To this purpose, the SKA Observatory is especially suited, thanks both to the enormous volumes it will probe, and to the variety and complementarity of cosmological observables that its surveys will make available to us.

gr-qc

Bifurcation of gravity-capillary Stokes waves with constant vorticity

We consider the gravity-capillary water waves equations of a 2D fluid with constant vorticity. By employing variational methods we prove the bifurcation of periodic traveling water waves -- which are steady in a moving frame -- for {\it all} the values of gravity, surface tension, constant vorticity, depth and wavelenght, extending previous results valid for restricted values of the parameters. We parametrize the bifurcating Stokes waves either with their speed or their momentum.

math.AP

KAM for reversible derivative wave equations

We prove the existence of Cantor families of small amplitude, analytic, quasi-periodic solutions of derivative wave equations, with zero Lyapunov exponents and whose linearized equation is reducible to constant coefficients. This result is derived by an abstract KAM theorem for infinite dimensional reversible dynamical systems

math.AP

Cantor families of periodic solutions for completely resonant nonlinear wave equations

We prove existence of small amplitude, $2π\slash \om$-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions, for any frequency $ \om $ belonging to a Cantor-like set of positive measure and for a new set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem. In spite of the complete resonance of the equation we show that we can still reduce the problem to a {\it finite} dimensional bifurcation equation. Moreover, a new simple approach for the inversion of the linearized operators required by the Nash-Moser scheme is developed. It allows to deal also with nonlinearities which are not odd and with finite spatial regularity.

math.AP

Forced vibrations of wave equations with non-monotone nonlinearities

We prove existence and regularity of periodic in time solutions of completely resonant nonlinear forced wave equations with Dirichlet boundary conditions for a large class of non-monotone forcing terms. Our approach is based on a variational Lyapunov-Schmidt reduction. It turns out that the infinite dimensional bifurcation equation exhibits an intrinsic lack of compactness. We solve it via a minimization argument and a-priori estimate methods inspired to regularity theory of Rabinowitz

math.AP

Bifurcation of free vibrations for completely resonant wave equations

We prove existence of small amplitude, 2 pi/omega -periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency omega belonging to a Cantor-like set of positive measure and for a generic set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem.

math.AP