Dynamics on Lorentz Manifolds.

2.12 Minkowski forms - basic definitionsChapter 3 Basic Differential Topology; 3.1 Some differential topological notions; 3.2 Inheritability of continuity and smoothness to leanike submanifolds; 3.3 Definition of prefoliation and foliation; 3.4 Preliminary results to the Frobenius Theorem; 3.5 Uniqueness in the Frobenius Theorem; 3.6 Passage from local to global in the Frobenius Theorem; 3.7 The Frobenius Theorem; 3.8 Potential submersions; 3.9 Lorentz metrics - basic definitions; Chapter 4 Basic Lie Theoretic Results; 4.1 Some Lie theoretic definitions and notation.

4.2 Dynamical consequences of the Frobenius Theorem4.3 exp Ad and ad; 4.4 The Lie group Lie algebra correspondence; 4.5 Some facts about Lie subgroups; 4.6 The Lie algebra of [AB]; 4.7 Lie groups and Lie algebras from bilinear and quadratic forms; 4.8 Abelian Lie groups; 4.9 Miscellaneous results; 4.10 Generalities on semisimple groups and algebras; 4.11 Real Jordan decomposition; 4.12 Consequences of results on real Jordan decomposition; 4.13 Generalities on algebraic groups; 4.14 Generalities on nilpotent groups and algebras; 4.15 Generalities on the nilradical.

4.16 Relationships between representation theoriesChapter 5 More Lie Theory; 5.1 Connection-preserving diffeomorphisms form a Lie group; 5.2 The isometry group of a pseudoRiemannian manifold is a Lie group; 5.3 More results on expansive sequences; 5.4 Lie groups densely embedded in other Lie groups; 5.5 Generalities on the Levi decomposition; 5.6 Large normalizers and centralizers; 5.7 Representation theory; Chapter 6 Minkowski Linear Algebra; 6.1 Notations for important elements and Lie subalgebras of so(Qd); 6.2 Linear algebra of Minkowski vector spaces; 6.3 Basic calculations.

6.4 Embeddings of Lorentz Lie algebrasChapter 7 Basic Dynamical Results; 7.1 Kowalsky's Lemma; 7.2 Higher jets of vector fields and metrics - notation; 7.3 Matrix realizations of jets and calculus on jets; 7.4 Miscellaneous results; 7.5 A basic collection of rigidity results; 7.6 Strongly lightlike and nontimelike vectors; 7.7 Basic results on degenerate orbits; 7.8 More on strongly lightlike and nontimelike vectors; 7.9 Nonproperness and cocompact subgroups; 7.10 Kowalsky subsets; 7.11 Types of chaotic actions; 7.12 Induction of actions: Definition; 7.13 Induction of actions: Basic results.