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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An abstract perturbation theorem for Fredholm sections on compact zero sets that preserves existing transversality and supports cobordism arguments, shown via re-proof of Schwarz's theorem on Hamiltonian action functionals.
A product-kernel interpolation method is proposed that augments state with parameters to produce symplectic large-step predictors for Hamiltonian dynamics by construction, with error bounds that extend from the non-parameterized case.
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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.