1,721,006 research outputs found
Stability and diffusion in Hamiltonian Systems Via Analytical and Variational Perturbative Methods
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On the measure of Lagrangian invariant tori in nearly-integrable mechanical systems
Full text linkConsider an n-degrees-of-freedom real-analytic mechanical system with potential
, x being a n-dimensional angle variable. Then, for ‘‘general’’ potentials f ’s and small
enough, the Liouville measure of the complementary of invariant tori is smaller than $\epsilon |\ln \epsilon|^a (for a suitable a > 0)
Low-order resonances in weakly dissipative spin-orbit models
No full textSecond-order differential equations with small nonlinearity and
weak dissipation, such as the spin–orbit model of celestial mechanics,
are considered. Explicit conditions for the coexistence of
periodic orbits and estimates on the measure of the basins of
attraction of stable periodic orbits are discussed
Exponential stability for the resonant D'Alembert model of Celestial Mechanics
No full textWe consider the classical D'Alembert Hamiltonian model for a rotationally symmetric planet revolving on Keplerian ellipse around a ̄xed star in an almost exact day/year" resonance and prove that, notwithstanding proper degeneracies, the system is stable for exponentially long times, provided the oblateness and the eccentricity are suitably small
On the stability of some properly-degenerate Hamiltonian systems with two degrees of freedom
No full textAbstract. Properly degenerate nearly–integrable Hamiltonian systems with two degrees of freedom such that the “intermediate system” depend explicitly upon the angle–variable conjugated to the non–degenerate action–variable are considered and, in particular, model problems motivated by classical examples of Celestial Mechanics, are investigated. Under suitable “convexity” assumptions on the intermediate Hamiltonian, it is proved that, in every energy surface, the action variables stay forever close to their initial values. In “non convex” cases, stability holds up to a small set where, in principle, the degenerate action–variable might (in exponentially long times) drift away from its initial value by a quantity independent of the perturbation. Proofs are based on a “blow up” (complex) analysis near separatrices, KAM techniques and energy conservation arguments
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