Invariant Manifolds, Entropy And Billiards; Smooth Maps With Singularities
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![Sophia Cahill twitter pictures backstage at LFW](http://i.dailymail.co.uk/i/pix/2012/02/28/article-0-11F49431000005DC-472_306x423.jpg)
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![A former Miss Wales, Sophia has been modelling since she was 18 but after getting pregnant with son Bailey, now nine - and splitting up with his father soon after - she turned to glamour modelling to pay the bills](http://i.dailymail.co.uk/i/pix/2012/02/28/article-2107637-11F58C63000005DC-423_306x619.jpg)
![A former Miss Wales, Sophia has been modelling since she was 18 but after getting pregnant with son Bailey, now nine - and splitting up with his father soon after - she turned to glamour modelling to pay the bills](http://i.dailymail.co.uk/i/pix/2012/02/28/article-2107637-11F58C58000005DC-571_306x619.jpg)
![Sophia Cahil](http://i.dailymail.co.uk/i/pix/2012/02/28/article-0-11F4FB1A000005DC-882_306x618.jpg)
![Sophia Cahill](http://i.dailymail.co.uk/i/pix/2012/02/28/article-0-11F4FADA000005DC-766_306x618.jpg)
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