By Morris W. Hirsch, Charles C. Pugh, Michael Shub (auth.)

ISBN-10: 3540081488

ISBN-13: 9783540081487

ISBN-10: 3540373829

ISBN-13: 9783540373827

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1 ) , Jf carries differentiable then I foh "I ( u ) - f ~ ' h -I (U)lh x = I J h x ( f ~ h - l ) - a h x ( f ° ' h-I )I = lim sup - u÷hx dx(U'hx) IJf(J)-Jf(J')l Clearly o, o' are represented by ]d J has a unique into itself, section}. " Jf-invariant ]d being s e c t i o n , say {jcJ: o]f: X0 ÷ J. j is representable by a For foh - l is d i f f e r e n t i a b l e whenever i n v a r i a n t section ~jf There is another ~ is. 3) the Jf ]d namely x ~ Jx(Of) I t is i n v a r i a n t because of is f#-invariant.

1). gives a d i f f e r e n t Finally, Then we go on to prove the l a m i - we show how the strong unstable m a n i f o l d theory way to c o n s t r u c t Wu. In §5A, we prove some c l a s s i c a l center m a n i f o l d theorems, not used in the r e s t o f the paper. A l i n e a r endomorphism of a Banach space Definition. hyperbolic i f i t s spectrum l i e s o f f the c i r c l e o f radius Corresponding to t h i s s p e c t r a l decomposition i s a El • E2. lies inside. into El . The spectrum o f E2 y E E2.

Jf-invariant ]d being s e c t i o n , say {jcJ: o]f: X0 ÷ J. j is representable by a For foh - l is d i f f e r e n t i a b l e whenever i n v a r i a n t section ~jf There is another ~ is. 3) the Jf ]d namely x ~ Jx(Of) I t is i n v a r i a n t because of is f#-invariant. Hence Jx(Of) = o j f ( x ) This proves t h a t : t i a b l e section, differentiable at each Hence f u n c t i o n at u n i f o r m l y bounded. bundle over of X. x c XO, the j e t of acts on L x x is d i f f e r e n t i a b l e I t remains to prove t h a t I t s f i b e r at x at of is representable by a d i f f e r e n x).

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Invariant Manifolds by Morris W. Hirsch, Charles C. Pugh, Michael Shub (auth.)


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