Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of invariant whiskered tori by a parameterization method.
  Part I: Maps and flows in finite dimensions   We present theorems which provide the existence of invariant whiskered tori
in finite-dimensional exact symplectic maps and flows. The method is based on
the study of a functional equation expressing that there is an invariant torus.
  We show that, given an approximate solution of the invariance equation which
satisfies some non-degeneracy conditions, there is a true solution nearby. We
call this an {\sl a posteriori} approach.
  The proof of the main theorems is based on an iterative method to solve the
functional equation.
  The theorems do not assume that the system is close to integrable nor that it
is written in action-angle variables (hence we can deal in a unified way with
primary and secondary tori). It also does not assume that the hyperbolic
bundles are trivial and much less that the hyperbolic motion can be reduced to
constant.
  The a posteriori formulation allows us to justify approximate solutions
produced by many non-rigorous methods (e.g. formal series expansions, numerical
methods). The iterative method is not based on transformation theory, but
rather on succesive corrections. This makes it possible to adapt the method
almost verbatim to several infinite-dimensional situations, which we will
discuss in a forthcoming paper. We also note that the method leads to fast and
efficient algorithms. We plan to develop these improvements in forthcoming
papers.

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The categories of this paper are: supr-con
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
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The categories of this paper are: stat
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph