Comptes Rendus
Ordinary differential equations/Dynamical systems
The flowbox theorem for divergence-free Lipschitz vector fields
[Le théorème du flot tubulaire pour les champs vectoriels Lipschitz à divergence nulle]
Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 881-886.

Dans cette note, nous prouvons le théorème du flot tubulaire pour les champs vectoriels Lipschitz à divergence nulle.

In this note, we prove the flowbox theorem for divergence-free Lipschitz vector fields.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.07.006
Mário Bessa 1

1 Universidade da Beira Interior, Rua Marquês d'Ávila e Bolama, 6201-001 Covilhã, Portugal
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Mário Bessa. The flowbox theorem for divergence-free Lipschitz vector fields. Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 881-886. doi : 10.1016/j.crma.2017.07.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.07.006/

[1] R. Abraham; J. Marsden Foundations of Mechanics, Benjamin/Cummings Publishing Co., Inc., Advanced Book Program, Reading, MA, USA, 1978

[2] A. Arbieto; C. Matheus A pasting lemma and some applications for conservative systems, Ergod. Theory Dyn. Syst., Volume 27 (2007), pp. 1399-1417 (With an appendix by David Diica and Yakov Simpson-Weller)

[3] C. Barbarosie Representation of divergence-free vector fields, Q. Appl. Math., Volume 69 (2011) no. 2, pp. 309-316

[4] M. Bessa The Lyapunov exponents of generic zero divergence three-dimensional vector fields, Ergod. Theory Dyn. Syst., Volume 27 (2007) no. 5, pp. 1445-1472

[5] M. Bessa; J. Rocha Removing zero Lyapunov exponents in volume-preserving flows, Nonlinearity, Volume 20 (2007) no. 4, pp. 1007-1016

[6] M. Bessa; J. Lopes-Dias Generic dynamics of 4-dimensional C2 Hamiltonian systems, Commun. Math. Phys., Volume 281 (2008) no. 3, pp. 597-619

[7] M. Bessa, M.J. Torres, P. Varandas, On the periodic orbits, shadowing and strong transitivity of continuous flows, Preprint, 2016.

[8] A. Boldt; C. Calcaterra Lipschitz flow-box theorem, J. Math. Anal. Appl., Volume 338 (2008), pp. 1108-1115

[9] H.E. Cabral On the Hamiltonian flow box theorem, Qual. Theory Dyn. Syst., Volume 12 (2013) no. 1, pp. 5-9

[10] F. Castro, F. Oliveira, On the Transitivity of Invariant Manifolds of Conservative Flows, Preprint ArXiv, 2015.

[11] B. Dacorogna; J. Moser On a partial differential equation involving the Jacobian determinant, Ann. Inst. Henri Poincaré, Volume 7 (1990) no. 1, pp. 1-26

[12] H. Federer Geometric Measure Theory, Springer-Verlag, 1969

[13] M.C. Irwin Smooth dynamical systems, Nonlinear Dyn., Volume 17 (2001) (World Scientific)

[14] R. Mañé Ergodic Theory and Differentiable Dynamics, Springer Verlag, 1987

[15] J. Moser On the volume elements on a manifold, Trans. Amer. Math. Soc., Volume 120 (1965), pp. 286-294

[16] J. Palis; W. de Melo Geometric Theory of Dynamical Systems – an Introduction, Springer-Verlag, New York, Berlin, 1982

[17] C. Robinson Lectures on Hamiltonian Systems, Monograf. Mat. Rio de Janeiro IMPA, 1971

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