By Alexandre J. Chorin, Jerrold E. Marsden
The aim of this article is to give a few of the uncomplicated rules of fluid mechanics in a mathematically beautiful demeanour, to give the actual heritage and motivation for a few structures which were utilized in fresh mathematical and numerical paintings at the Navier-Stokes equations and on hyperbolic platforms and to curiosity many of the scholars during this appealing and tough topic. The 3rd variation has integrated a couple of updates and revisions, however the spirit and scope of the unique e-book are unaltered.
Read or Download A Mathematical Introduction to Fluid Mechanics (3rd Edition) (Texts in Applied Mathematics, Volume 4) PDF
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Extra info for A Mathematical Introduction to Fluid Mechanics (3rd Edition) (Texts in Applied Mathematics, Volume 4)
J Math Anal Appl 189:462–490 Chapter 4 A Boundary Crisis in High Dimensional Chaotic Systems Ling Hong, Yingwu Zhang, and Jun Jiang Abstract A crisis is investigated in high dimensional chaotic systems by means of generalized cell mapping digraph (GCMD) method. The crisis happens when a hyperchaotic attractor collides with a chaotic saddle in its fractal boundary, and is called a hyperchaotic boundary crisis. In such a case, the hyperchaotic attractor together with its basin of attraction is suddenly destroyed as a control parameter passes through a critical value, leaving behind a hyperchaotic saddle in the place of the original hyperchaotic attractor in phase space after the crisis, namely, the hyperchaotic attractor is converted into an incremental portion of the hyperchaotic saddle after the collision.
The Poincare mapping relative to the Neimark bifurcation of the period-1 solution of positive mapping (or negative mapping) at a D 0:85 and b D 1 is presented in Fig. 4a. 0:4237; 0:4237/ is the point for the period-1 solution of PC point xk ; yk or P relative to the Neimark bifurcation. 1. 1:0597; 0:4237/ is the biggest boundary for with the initial condition xk ; yk the strange attractors around the period-1 solutions with the Neimark bifurcation. The skew symmetry of the strange attractors in the Poincare mapping section is observed.
Cambridge University Press, Cambridge 14. Hsu CS (1995) Global analysis of dynamical systems using posets and digraphs. Int J Bifurcat Chaos 5(4):1085–1118 15. Hong L, Xu JX (1999) Crises and chaotic transients studied by the generalized cell mapping digraph method. Phys Lett A 262:361–375 16. Hong L, Xu JX (2001) Discontinuous bifurcations of chaotic attractors in forced oscillators by generalized cell mapping digraph (GCMD) method. Int J Bifurcat Chaos 11:723–736 17. Hong L, Sun JQ (2006) Codimension two bifurcations of nonlinear systems driven by fuzzy noise.
A Mathematical Introduction to Fluid Mechanics (3rd Edition) (Texts in Applied Mathematics, Volume 4) by Alexandre J. Chorin, Jerrold E. Marsden