By William Burke

This can be a self-contained introductory textbook at the calculus of differential varieties and glossy differential geometry. The meant viewers is physicists, so the writer emphasises purposes and geometrical reasoning so one can supply effects and ideas an actual yet intuitive that means with no getting slowed down in research. the massive variety of diagrams is helping elucidate the basic rules. Mathematical subject matters lined contain differentiable manifolds, differential varieties and twisted varieties, the Hodge famous person operator, external differential structures and symplectic geometry. the entire arithmetic is influenced and illustrated by means of worthwhile actual examples.

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Sur le chaos multiplicatif. Ann. Sci. Math. Que. : Positive martingales and random measures. Chi. Ann. Math. : Sur certaines martingales de B. Mandelbrot Adv. Math. : Multiplications aléatoires et dimensions de Hausdorff. Ann. Inst. Henri Poincaré Probab. Stat. : Produits de poids aléatoires indépendants et applications. In: Fractal Geometry and Analysis (Montreal, PQ, 1989), pp. 277–324. NATO Adv. Sci. Inst. Ser. C Math. Phys. , vol. 346. : Fractal structure of 2Dquantum gravity. Mod. Phys. : Précisions sur la structure locale de la turbulence dans un fluide visqueux aux nombres de Reynolds élevés, Mécanique de la turbulence, Colloq.

Adv. Math. : KPZ in one dimensional random geometry of multiplicative cascades. Commun. Math. Phys. : Lévy Processes. : Martingale convergence in the branching random walk. J. Appl. Probab. : Growth rates in the branching random walk. Z. Wahrsch. Verw. Geb. : Uniform convergence of martingales in the branching random walk. Ann. Probab. : Seneta-Heyde norming in the branching random walk. Ann. Probab. : Measure change in multitype branching. Adv. Appl. Probab. : The smoothing transform: the boundary case.

Fully developed turbulence and intermittency in turbulence. Proceedings of the International School of Physics “Enrico Fermi”. In: Ghil, M. ) Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics, course 88, pp. 84–88. : Sur une extension de la notion de loi semi-stable. Ann. Inst. Henry Poincaré Probab. Stat. : Multifractal dimensions and scaling exponents for strongly bounded random fractals. Ann. Appl. Probab. : Minimal position and critical martingale convergence in branching random walks, and directed polymers on disordered trees.