One-parameter group of transformations

  • #1

Main Question or Discussion Point

I'm trying to understand what a one-parameter group of transformations really is. At one lecture I was told that they are trivial lie groups. In Arnold's "Ordinary Differential Equations" they are defined as an action by the group of real numbers; a collection of transformations parametrised by the real parameter t (time), and as being the mathematical equivalent of a two-sided deterministic process. I can more or less understand all this, but still feel some confusion. For example, is there such a thing as a two-parameter group of transformations? n-parameter?
 

Answers and Replies

  • #2
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Yes, there are multiparameter Lie groups of transformations. But they are more complex in their structure; in particular, they are isomorphic with systems of PDEs, not of ODEs as the one-parameter groups are.
 

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