By Isaac M. Khalatnikov, Isaac Markovich Khalatnikov
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Extra info for An introduction to the theory of superfluidity
ITN-1 lim ** 1 rCPx) n=o providhd bath t h e l i m i t in t h e numerator and l i m i t in t h e denominator exist. If f and T were continuous, an ergodic theorem for ip would say that both numerrrtor and denominator exist f o r almost a l l 5 and a r e essentially independent of f o r t h e l i m i t on t h e l e f t . it approaches i n f i n i t y as x; t h e same would then follow Unfortunately, r x approaches (x) is not continuous; Z.
S The extended t o A_' i s - it permits I: are mapped by cb A) so but t h e reflection sends C t o t h e v i c i n i t y of B' S into itself. is a n o t h v advantage t o making the identification be defined on all of cb whenever This leaves only half of t h e picture The shaded reglm running f m m reflected t o run froln cb by . to A, There 6 to either near i sends may therefore be extended into i t s e l f , sending the arc may be visualized as obtained by t h e following three steps: 1. Stretch S out t o roughly twice i t s original length, while shrinking it l a t e r a l l y .
It i s , on the other hand, hard t o verify in practical applications and non-trivi a l examples axe r e l a t i v e l y scarce. It i s a t t h i s time s t i l l too early t o decide whether Axiom A as it stands is too r e s t r i c t i v e t o apply t o cases of i n t e r e s t , but e i t h e r it o r some weakened version of it seems l i k e l y t o p l w en important r o l e i n future developments. It may be helpful t o note here one difference between hyperbolic fixed points and more general hyperbolic sets.
An introduction to the theory of superfluidity by Isaac M. Khalatnikov, Isaac Markovich Khalatnikov