Timeline for Example of n-parameter family of real-analytic diffeomorphisms acting on $S^3$, constant on the Hopf fibres

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Feb 2, 2014 at 13:25	comment	added	Robert Bryant		Maybe you want something else, but, why not take the $3$-parameter group of isometries of $S^3$ that consists of left multiplication by elements of $\mathrm{SU}(2)$ (these commute with $\phi_t$). That has your desired properties. If you want your family to be parametrized by the $3$-torus, just take any real analytic mapping $f:T^3\to SU(2)$ that is surjective, and you are done. It can be done with $n=2$ if you want to work a little harder, but you can't get down to $n=1$, obviously.
Feb 2, 2014 at 7:53	history	edited	user42388	CC BY-SA 3.0	edited body
Feb 2, 2014 at 7:21	history	edited	user42388	CC BY-SA 3.0	added 56 characters in body
Feb 2, 2014 at 6:55	comment	added	Daniele Zuddas		Your second condition doesn't make much sense, because $f_{\theta_i}$ is a diffeomorphim, so $x = y$. Please reformulate the question.
S Feb 2, 2014 at 5:38	history	suggested	gaoxinge	CC BY-SA 3.0	more clear
Feb 2, 2014 at 5:35	review	Suggested edits
S Feb 2, 2014 at 5:38
Feb 2, 2014 at 4:46	review	First posts
Feb 2, 2014 at 4:47
Feb 2, 2014 at 4:27	history	asked	user42388	CC BY-SA 3.0