An abstract KAM theorem is developed for infinitely many weakly interacting particles with decaying masses, enabling construction of full-dimensional invariant tori in infinite-dimensional systems with long-range interactions.
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Under a domination condition, real-analytic deformations of symplectomorphism products yield large robustly transitive sets and new non-uniformly-hyperbolic examples via blender-horseshoe perturbations and control-theory ideas.
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Kolmogorov invariant torus theorem for weakly interacting particles I: Full dimensional tori
An abstract KAM theorem is developed for infinitely many weakly interacting particles with decaying masses, enabling construction of full-dimensional invariant tori in infinite-dimensional systems with long-range interactions.
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Robustly transitive behavior in symplectic dynamics
Under a domination condition, real-analytic deformations of symplectomorphism products yield large robustly transitive sets and new non-uniformly-hyperbolic examples via blender-horseshoe perturbations and control-theory ideas.