use CSS3 transforms/transitions. This is a lot faster and better than using javascript or a JS library such as jQuery. see here
If you want more detailed animations, use CSS3 animations. see here
And most importantly, to ensure full cross-plat support of CSS3, install Modernizr and run some shims. see here
EDIT: If you want to trigger the above CSS3 with iOS touch gestures functions, then define those styles inside of the functions.