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DTSTART:20250330T030000
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DTSTAMP:20260425T075314Z
UID:66a376b9cc414375108087@ist.ac.at
DTSTART:20250211T140000
DTEND:20250211T153000
DESCRIPTION:Speaker: Dongchen Li\nhosted by Kaloshin Group\nAbstract: A ble
 nder is a hyperbolic basic set such that the projection of its stable/unst
 able set onto some central subspace has a non-empty interior and thus has 
 a higher topological dimension than the set itself.We show that\, for any 
 symplectic Cr-diffeomorphism (where r is sufficiently large and finite\, o
 r r=\,) of a 2N-dimensional (N>1) symplectic manifold\, symplectic blender
 s can be obtained by an arbitrarily small symplectic perturbation near any
  one-dimensional whiskered KAM-torus that has a homoclinic orbit. Using th
 is result\, we prove that non-transverse homoclinic intersections between 
 invariant manifolds of a saddle-center periodic point (i.e.\, it has exact
 ly one pair of complex multipliers on the unit circle) are persistent in t
 he following sense: the original map is in the Cr closure of a C1 open set
  in the space of symplectic Cr-diffeomorphisms\, where maps having such sa
 ddle-center homoclinic intersections are dense. These results also hold fo
 r Hamiltonian flows in the corresponding settings.
LOCATION:Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101
 )\, ISTA
ORGANIZER:cfrancois@ist.ac.at
SUMMARY:Dongchen Li: Symplectic blenders near whiskered tori and persistenc
 e of saddle-center homoclinics
URL:https://talks-calendar.ista.ac.at/events/5137
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