Ali _Taghavi
11-16-2005, 03:52 AM
Hello
I am intersted in the second part of the Hilbert 16th Problem which main object is the number of limit cycles of a polynomial vector field.By limit cycle I mean an isolated periodic trajectory of a vector field on the Plane,in fact a limit cycle is an isolated compact invariant set for a vector field,and homeomorph to S^1
since two years ago,I found various papers on "quantum theory" which focuse on "limit cycle" theoretical aspects of QM:
For Example:
Cetto and De La Penna:"Is Quantum mechanics a limit cycle theory"1995 Kluwer,Fundamental Problems of Quantum Physics
Glazek and Wilson "limit cycles in Quantumn theories" Phys. Review .Letter 2002
I want to understand the meaning of "limit cycle" in such Physical Papers.Is such "limit cycle" the same limit cycles in the second part of the Hilbert 16th Problem?
Further It seems that existence of compact invariant sets for the Vector Field X on the plane, is the only obstruction for Weyl (Quantum) formula XS-SX=1 where S is a linear operator on C^inf(R^2) and X is the lie derivative operator on C^inf(R^2),what is the consequence of this obstruction(to XS-SX=1)(both Physical and Mathematical consequense):
please see the following too:
http://mathforum.org/kb/thread.jspa?threadID=1295185&messageID=4079599#4079599
Finally,I search for an infinit dimensional nature for the Hilbert 16th Problem(and somehow a mathematical quantization of this problem)
your comments are very appreciated
Thank you
Ali Taghavi
I am intersted in the second part of the Hilbert 16th Problem which main object is the number of limit cycles of a polynomial vector field.By limit cycle I mean an isolated periodic trajectory of a vector field on the Plane,in fact a limit cycle is an isolated compact invariant set for a vector field,and homeomorph to S^1
since two years ago,I found various papers on "quantum theory" which focuse on "limit cycle" theoretical aspects of QM:
For Example:
Cetto and De La Penna:"Is Quantum mechanics a limit cycle theory"1995 Kluwer,Fundamental Problems of Quantum Physics
Glazek and Wilson "limit cycles in Quantumn theories" Phys. Review .Letter 2002
I want to understand the meaning of "limit cycle" in such Physical Papers.Is such "limit cycle" the same limit cycles in the second part of the Hilbert 16th Problem?
Further It seems that existence of compact invariant sets for the Vector Field X on the plane, is the only obstruction for Weyl (Quantum) formula XS-SX=1 where S is a linear operator on C^inf(R^2) and X is the lie derivative operator on C^inf(R^2),what is the consequence of this obstruction(to XS-SX=1)(both Physical and Mathematical consequense):
please see the following too:
http://mathforum.org/kb/thread.jspa?threadID=1295185&messageID=4079599#4079599
Finally,I search for an infinit dimensional nature for the Hilbert 16th Problem(and somehow a mathematical quantization of this problem)
your comments are very appreciated
Thank you
Ali Taghavi