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UID:dd8996d49533788a0b1eaa484ba59432
CATEGORIES:Applied and Computational Math Seminar
CREATED:20231115T143356
SUMMARY:Methods of Geometric Control in Hamiltonian Dynamics
LOCATION:Hill 705
DESCRIPTION:<p><span style="border: 0px; font-style: normal; font-weight: 400; font-siz
 e: 12pt; line-height: inherit; font-family: Calibri, Helvetica, sans-serif;
  margin: 0px; padding: 0px; vertical-align: baseline; letter-spacing: norma
 l; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; wi
 dows: 2; word-spacing: 0px; white-space: normal;">We consider an integrable
  Hamiltonian system subject to a small, time-periodic perturbation.&nbsp;</
 span><span style="border: 0px; font-style: normal; font-weight: 400; font-s
 ize: 12pt; line-height: inherit; font-family: Calibri, Helvetica, sans-seri
 f; margin: 0px; padding: 0px; vertical-align: baseline; letter-spacing: nor
 mal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; 
 widows: 2; word-spacing: 0px; white-space: normal;">We assume that the pert
 urbed system has a normally hyperbolic invariant manifold (NHIM) whose stab
 le and unstable manifolds intersect transversally. Associated to each trans
 verse intersection one can define a scattering map, which gives the future 
 asymptotic of a homoclinic orbit as a function of its past asymptotic. &nbs
 p;We assume that we have a system of such scattering maps.&nbsp;</span><spa
 n style="border: 0px; font-style: normal; font-weight: 400; font-size: 12pt
 ; line-height: inherit; font-family: Calibri, Helvetica, sans-serif; margin
 : 0px; padding: 0px; vertical-align: baseline; letter-spacing: normal; orph
 ans: 2; text-align: left; text-indent: 0px; text-transform: none; widows: 2
 ; word-spacing: 0px; white-space: normal;">We provide results on the geomet
 ric controllability of the system. We show that, under explicit conditions 
 on the scattering maps and on the inner dynamics (restricted to the NHIM), 
 &nbsp;for any two points on the NHIM, there is an orbit of the Hamiltonian 
 flow that goes from near the first point to near the second point. &nbsp;Al
 so, for any path on the NHIM, there is an orbit of the Hamiltonian flow tha
 t shadows that path. &nbsp;The upshot is that we use the perturbation as a 
 controller.</span></p>
CONTACT:Marian Gidea (Yeshiva University)
DTSTAMP:20260829T215201
DTSTART;TZID=America/New_York:20231121T110000
DTEND;TZID=America/New_York:20231121T120000
SEQUENCE:0
TRANSP:OPAQUE
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