Serge Aubry - Physics Department . Technion
Serge Aubry - Physics Department . Technion Serge Aubry - Physics Department . Technion
Almost Periodic Solutions: Fröhlich, Spencer, Wayne (1986) Assume C p,p’ depends only on µ p and µ p’ (pair interactions) Then, with large probability, there are quasiperiodic lattice vibrations of finite total energy which lie on some infinitedimensional, compact invariant tori in phase space. Serge Aubry, Aubry, LLB, FRANCE
Quasiperiodic Periodic Solutions: Bourgain Wang (2008) In random DNLS, there are quasiperiodic solution corresponding to finite dimension invariant tori Almost periodic Periodic Solutions: Walter Craig (private communication) In random DNLS, there are « many » almost periodic solutions corresponding to infinite dimension invariant tori (use of Nash-Moser method?) Serge Aubry, Aubry, LLB, FRANCE
- Page 1 and 2: Suppression of Energy Diffusion in
- Page 3 and 4: I-Nonlinear spatially periodic syst
- Page 5 and 6: Initial wavepacket Time periodic so
- Page 7 and 8: II- Exact Time Periodic Solutions (
- Page 9 and 10: Numerical Calculation of Localized
- Page 11 and 12: RDNLS: a straightforward proof of e
- Page 13: Anderson Representation of DNLS nor
- Page 18 and 19: The probability to find an initial
- Page 20 and 21: Assume the wavepacket spreads unifo
- Page 22 and 23: Example: What is the behavior of a
- Page 24 and 25: V Diffusion of a Wavepacket in nonl
- Page 26 and 27: There are initial conditions with n
- Page 28 and 29: VI-New Numerical Investigations G.
- Page 30 and 31: Serge Aubry, Aubry, LLB, FRANCE t=1
- Page 32 and 33: Participation number of norm distri
- Page 34 and 35: Serge Aubry, Aubry, LLB, FRANCE Tim
- Page 36 and 37: Scenario for the Absence of spreadi
- Page 38 and 39: Warning about the problem of reliab
- Page 40 and 41: VII Summary and concluding remarks
Almost Periodic Solutions:<br />
Fröhlich, Spencer, Wayne (1986)<br />
Assume<br />
C p,p’ depends only on µ p and µ p’ (pair interactions)<br />
Then, with large probability, there are quasiperiodic lattice<br />
vibrations of finite total energy which lie on some infinitedimensional,<br />
compact invariant tori in phase space.<br />
<strong>Serge</strong> <strong>Aubry</strong>, <strong>Aubry</strong>,<br />
LLB, FRANCE
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