Dynamics of two-dimensional time-periodic Euler fluid flows

Topology and its Applications

Volumn 152, Issue 1-2 SPEC. ISS., 2005, Pages 87-106

  Boyland, Philip ^a  

^a UNIVERSITY OF FLORIDA   (United States)

Author keywords

Euler fluid flows; Nielsen Thurston theory; Vorticity

Indexed keywords

EID: 23844516823     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.topol.2004.08.017     Document Type: Article

References (42)

1. R. Abraham J. Marsden T. Ratiu Manifolds, Tensor Analysis, and Applications 1988 Springer Berlin
2. V. Arnol'd B. Khesin Topological Methods in Hydrodynamics 1998 Springer Berlin
3. G.K. Batchelor An Introduction to Fluid Mechanics 1967 Cambridge University Press Cambridge
4. J. Birman Braids, Links and Mapping Class Groups Ann. of Math. Stud. 1975 Princeton University Press Princeton, NJ
5. J. Birman A. Libgober (Eds.) Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Artin's Braid Group Contemp. Math. vol. 78 1988
6. J. Birman R. Williams Knotted periodic orbits in dynamical systems. II: Knot holders for fibered knots in: Contemp. Math. vol. 20 1983 1-60
7. P. Boyland Topological methods in surface dynamics Topology Appl. 58 1994 223-298
8. P. Boyland Fluid mechanics and mathematical structures in: R.L. Ricca (Ed.) An Introduction to the Geometry and Topology of Fluid Flows in: NATO ASI Series: Mathematics 2001 Kluwer Academic Dordrecht 105-134
9. P. Boyland H. Aref M. Stremler Topological fluid mechanics of stirring J. Fluid Mech. 403 2000 277-304
10. P. Boyland H. Aref M. Stremler Topological fluid dynamics of point vortex motions Physica D 175 2003 69-95
11. Y. Brenier Topics on hydrodynamics and volume preserving maps in: Handbook of Mathematical Fluid Dynamics II 2003 North-Holland Amsterdam 55-86
12. M. Brown R. Samelson Particle motion in vorticity-conserving, two-dimensional incompressible flows Phys. Fluids 6 1994 2875-2876
13. A. Casson S. Bleiler Automorphisms of Surfaces after Nielsen and Thurston London Math. Soc. Stud. Texts vol. 9 1988 Cambridge University Press Cambridge
14. J.-Y. Chemin Fluides parfaits incompressibles Astérisque 230 1995
15. J. Etnyre R. Ghrist Stratified integrals and unknots in inviscid flows in: Contemp. Math. vol. 246 1999 99-112
16. A. Fathi F. Lauderbach V. Poenaru Travaux de Thurston sur les surfaces Astérique 66-67 1979
17. M. Finn S. Cox H. Byrne Topological chaos in inviscid and viscous mixers J. Fluid Mech. 493 2003 345-361
18. J. Franks Rotation numbers and instability sets Bull. Amer. Math. Soc. 40 2003 263-279
19. J. Franks M. Handel Periodic points of Hamiltonian surface diffeomorphisms Geom. Topology 7 20 2003 713-756
20. G. Gallavotti Foundations of Fluid Mechanics 2002 Springer Berlin
21. R. Ghrist R. Komendarczyk Topological features of inviscid flows in: R.L. Ricca (Ed.) An Introduction to the Geometry and Topology of Fluid Flows in: NATO ASI Series: Mathematics 2001 Kluwer Academic Dordrecht 183-202
22. C. He L. Hsiao Two-dimensional Euler equations in a time dependent domain J. Differential Equations 163 2000 265-291
23. M. Hirsch Differential Topology 1976 Springer Berlin
24. A. Katok Bernoulli diffeomorphisms on surfaces Ann. of Math. 110 1979 529-547
25. A. Katok Lyapunov exponents, entropy and periodic orbits for diffeomorphisms Publ. Math. IHES 51 1980 137-173
26. H. Koch Transport and instability for perfect fluids Math. Ann. 323 2002 491-523
27. Hideo Kozono On existence and uniqueness of a global classical solution of the two-dimensional Euler equation in a time-dependent domain J. Differential Equations 57 1985 275-302
28. A. Majda A. Bertozzi Vorticity and Incompressible Flow 2002 Cambridge University Press Cambridge
29. C. Marchioro M. Pulvirenti Mathematical Theory of Incompressible Non-Viscous Fluids 1994 Springer Berlin
30. Y. Matsumoto An Introduction to Morse Theory 2002 American Mathematical Society Providence, RI
31. D. McDuff D. Salamon Introduction to Symplectic Topology 1995 Oxford University Press Oxford
32. J. Milnor A note on curvature and the fundamental group J. Differential Geom. 2 1968 1-70
33. J. Milnor Morse Theory 1969 Princeton University Press Princeton, NJ
34. J. Moser On the volume elements on a manifold Trans. Amer. Math. Soc. 120 1965 286-294
35. J. Moser Stable and random motions in dynamical systems Ann. of Math. Stud. vol. 77 1973 Princeton University Press Princeton, NJ
36. L. Polterovich The Geometry of the Group of Symplectic Diffeomorphisms 2001 Birkhäuser Basel
37. A. Shnirelman Diffeomorphisms, braids, and flows in: R.L. Ricca (Ed.) An Introduction to the Geometry and Topology of Fluid Flows in: NATO ASI Series: Mathematics 2001 Kluwer Academic Dordrecht 253-270
38. J. Serrin Mathematical principles of classical fluid mechanics Handbuch Phys. VIII 1 1959
39. W. Thurston On the geometry and dynamics of diffeomorphisms of surfaces Bull. Amer. Math. Soc. 19 1988 417-431
40. A. Vikhansky Simulation of topological chaos in laminar flow Chaos 2004 in press
41. 2 with positive topological entropy. A remark on: "Planar homoclinic points" by D. Pixton and "On the generic existence of homoclinic points" by F. Oliveira J. Statist. Phys. 80 1995 481-485
42. L.-S. Young Entropy of continuous flows on compact 2-manifolds Topology 16 1977 469-471