We consider the perturbed relativistic Kepler problem d/dt ( m x' / sqrt{1-|x'|^2/c^2} ) = -α x / |x|^3 + ε ∇_x U(t,x), x ∈ R^2 {0}, where m, α > 0, where c is the speed of light, and U(t,x) is a function T-periodic in the first variable. For ε > 0 sufficiently small, we prove the existence of T-periodic solutions with prescribed winding number, bifurcating from invariant tori of the unperturbed problem.
Periodic solutions to a perturbed relativistic Kepler problem
Feltrin, Guglielmo
2021-01-01
Abstract
We consider the perturbed relativistic Kepler problem d/dt ( m x' / sqrt{1-|x'|^2/c^2} ) = -α x / |x|^3 + ε ∇_x U(t,x), x ∈ R^2 {0}, where m, α > 0, where c is the speed of light, and U(t,x) is a function T-periodic in the first variable. For ε > 0 sufficiently small, we prove the existence of T-periodic solutions with prescribed winding number, bifurcating from invariant tori of the unperturbed problem.File in questo prodotto:
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