Table of Contents for
Variational Methods

Variational Methods by Thomas Haberkorn, Jean-Baptiste Caillau, Christoph Schnörr, Gabriel Peyré, Maïti Variational Methods

Cover
Title Page
Copyright
Contents
Part I
Part II
Index

Search in book...
Toggle Font Controls
Create new playlist

Name your new playlist

Playlist description (optional)
Sign In

Email address

Password

Forgot Password?

or

Continue with Facebook

Continue with Google
Sign Up

Full Name

Email address

Confirm Email Address

Password

or

Continue with Facebook

Continue with Google

Prev Previous Chapter

Index

Endnotes

Complete results (text files, movies, other examples) and MATLAB© code, are available at http://maitinebergounioux.net/PagePro/Movies.html.

One can look at http://maitinebergounioux.net/PagePro/Movies.html to see the convergence process.

A codec is a system for image coding and decoding.

http://numod.ins.uni-bonn.de/software/quocmesh/

www.tft.lth.se/video/co_operation/data_exchange/

ftp://ftp.ira.uka.de/pub/vid-text/image_sequences/

OASIS online database, http://www.oasis-brains.org/.

Thank you Gianna for proving stronger than the glass doors at RICAM!

Recall that, in Dynamical Systems, a path γ : ℝ → X on a manifold is quasiperiodic (of some rank≤ k) if there exists ω ∈ ℝk and a map Γ : ?k → X such that γ(t) = Γ(tω). Provided γ is smooth enough,γ then admits a Fourier expansion of the form γ(t) = Σj∈ℤk γjei2π (j⋅ω) t (in some local coordinates in atubular neighborhood of γ(ℝ)).

Conventionally, if f is a map from an open set U of a vector space E into another vector space F, wedefine f ′(x) as an element of F ⊗ E ∗ (as opposed to E ∗ ⊗ F), and we write f ′(x) ⋅ ξ for the contractionwith a vector ξ ∈ E. Also, we identify ℝn with its dual, so that S′(θ) may be imaged as the gradient ofS.

We use the ℓ∞-norm on ℝn (consistantly with the ℓ1-norm already used on the dual space ℤn).

A better, but less transparent, choice of norms lets C' = Cst/γ instead.

Thank you Jean-Christophe Yoccoz for drawing my attention to a mistake in a prior version of thisstatement.

There is no intrinsic (n −1)-dimensional Lebesgue measure, but the fact of having a positive (n −1)-dimensional Lebesgue measure is intrinsic.

The terminology we have chosen here is not standard. Related (but not always equivalent) conditions have been called essentially nonplanar, Rüssmann-nondegenerate, weakly nondegenerate,curved, etc.

Poincaré calls this square matrix the “bordered Hessian” of H [76].

Traditionally given the ununderstandable name of mean motions.

Thank you Gabriella Pinzari for pointing out to me the second kind of monomials too is ruled outby d’Alembert’s relations.

Note that our structural functions and the Reeb vector field differs by sign with respect to the analogous objects in [1, 10]. Therefore, our formula for κ is slightly different than the formulae in [1, 10].However, it is the same invariant.

Up to a translation by h, the positive cone generated by the zeros of ε0 in Sκ precisely correspondsto the conical subset whose neighborhood one wants to exclude.

Mather’s formulation of the conjecture is indeed more precise and involved.

A finite number of double resonance points contained in the simple resonance curves also have tobe taken into account.

The proof in the discrete setting is deduced from the continuous one by usual suspension processes,or follows along the same lines at the cost of more involved computations.

This map coincides with the scattering map of [11],we use here the term “homoclinic map” to matchwith the terminology of [18].

- Add Highlight
No Comment

..................Content has been hidden....................

You can't read the all page of ebook, please click here login for view all page.

Table of Contents for Variational Methods

Create new playlist

Sign In

Sign Up

Table of Contents for
Variational Methods