Estimates and Control of Diffeomorphisms in Contact Dynamical System

Abstract:

This paper studies the estimates and control of strictly contact diffeomorphisms in contact dynamical system. By constructing reparameterizing methods for contact system and using some perturbation techniques in Hamiltonian mechanics, this paper proves that the two norms of strictly contact diffeomorphism coincide under a certain condition and gives a variational descriptions of the tine one strictly contact isotopy.

• Periodical: Advanced Materials Research (Volume 529)
• Pages: 236-239
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.529.236
• Online since: June 2012
• Authors: Da Wei Sun
• Keywords: Contact Diffeomorphisms, Contact Dynamical System, Contact Energy

References

[1] A. Banyaga, P. Donato: Ann. Global Anal. Geom vol. 30(2006), pp.299-312.

[2] A. Banyaga, P.W. Spaeth: Information on http: /arxiv. org/abs/0812. 2461.

[3] A. Banyaga: Topology and Geometry, Ens. Math vol. 26 (1979), pp.47-53.

[4] H. Hofer, E. Zehnder: Symplectic Invariants and Hamiltonian Dynamics. (Berlin: Birkhauser Verlag, Basel. Boston, 1994).

[5] D. McDuff: Ann of Math Vol 141(1995), pp.349-371.

[6] C. Viterbo: Int Math Res Not Vol (2006), pp.349-371.

[7] Z. Han: Trans. Amer. Math. Soc. Vol 361 (2009), 3343-3357.

[8] Y. G. Oh, : J Symp Geom Vol 5(2007), pp.167-220.

[9] L. Polterovich: The geometry of the Group of Symplectic Diffeomorphism. (Berlin: Birkhauser Verlag, Basel. Boston, 2001).

[10] L. Buhovsky and Y. Ostrover: Geom. Funct. Anal. Vol 21(2011) pp.1296-1330.

DOI: 10.1007/s00039-011-0143-6