Invariants of Nearly Periodic Hamiltonian Systems

Abstract

Downloaded 22 Oct 2012 to 136.159.235.223. Redistribution subject to AIP license or copyright; see http://jmp.aip.org/about/rights_and_permissions WIGHTMAN FUNCTIONS 2029Hausdorff topological space which is locally homeomorphic to an open subset of em. One pictures 2) as lying above its projection ~ into em. The projection f of a point P of 2) furnishes coordinates for that point. It is possible that several points of 2) project into the same point f of~. If the projection map is a global homeomorphism, then 2) is a schlicht domain (single sheeted). If 2)1' 2)2 are two domains over em and 2)1 can be mapped continuously into a subset of 2)2 so that corresponding points have the same coordinates, we say 2)1 lies inside (liegt im innern) 2)2 and write 2)1 < 2)2' Although 2)1 < 2)2, it is possible that 2)1 is more ramified (has more sheets) than 2)2' For schlicht domains 2)1 < 2)2 means the same as 2)1 c 2)2' Suppose ~ is a domain over em, such that ~ < 2)" for each of a set {2),,} of domains over em. Then, if P is a point of~, the projection preserving continuous map in the definition of < gives an image point PIX

Effects of Aging Temperature on the Formation of Secondary Defects in Quenched α-Brass

“…non-linear vector fields X or Y, we must include perturbation techniques in our approach. An appropriate perturbation technique is that developed by Kruskal (Kruskal 1962, McNamara and Whiteman 1967, Rae and Davidson 1973, Kummer 1971. Another technique, closely related to that of Kruskal, was developed by Moser (Moser 1966, 1967, Kummer 1971.…”

“…Kruskal (Kruskal 1962, McNamara andWhiteman 1967) has considered an autonomous system of differential equations x = F ( x , E ) where it is assumed that for E = 0 the point x ( t ) traces out closed curves as t increases. Then one can introduce new variables y ( y = (yl, .…”

Equilibrium and stability in strongly inhomogeneous plasmas

“…Neglect of e* gives a V which is simpler to analyse graphically (setting c = m i » 1), V(x|P) = ^[P-A sc (x)] . (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) In Tormac or mirror machines, where * comes from the escape of electrons along field lines, e*~T , and so for a hot-ion plasma, e*~T << T.…”

“…From (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18), we see that V(x|P) is just half the square of the distance, in the P -A plane, from the point P which characterize a sc given particle, to the point A (x) on the trajectory. Externa of this distance, i.e.…”

“…, points A(x) at which Eq. (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) is satisfied, occur when sc sc the line passing from £ to A (x) is normal to the trajectory A at _A (x). Therefore all points P lying along this line have the same guidirg center position.…”