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chaotic attractors Homoclinic classes Lorenz attractor Lorenz-like attractor Singular Hyperbolic Attractors Expansive atratores hiperbolicos-singulares Singular Horseshoe saddle-node bifurcation atrator de Lorenz Maximal transitive sets Stability robustly expansive Circle Maps decaimento de correlacao Boundary Manifolds infinite-modal maps strange attractors Morse-Smale vector fields Ciclo Singular - Explosao Transitive sets spectral decomposition singular hyperbolic sets decay of correlations non uniformly expanding maps Singular hyperbolicity Variedades Com Bordo Fields Mixing homoclinic loops volume Ergodico Lorenz-like flow singular-hyperbolic attractors Folheacoes estaveis difeomorfismos comutativos Bilhares o Teorema de Fubini Campo de Vector bilhares com mesa com cuspide nao compacta Fluxos CW-expansivos global attractors sensitive dimensão de fractais Lorenz'attractor Breaking Ciclo Singular - Explocao Ciclo Singular Declinado Robust Singular Sets Singular Cycles Changing rotation intervals Mixing attractors inclination flip homoclinic loop Lyapunov stability Dichotomy expanding Lorenz attractors Bernoulli maps contracting Lorenz attractors statistical stability large deviation entropy-expansiveness Scaling Rate variational principle mesas de bilhar transformacao beta atracao focal geometria ODE solver Lorenz geometric flow pontos fixo comum endomorfismos do circulo Bilhares semi-dispersivos Teorema de Roklin volume zero Produto cruzado Fluxos Expansivos Bifurcation spiraling attractors vector fields Intervals Cycles Superficie Selada Quase-Transversal global chotic behavior Inclinacao Rapida boundary of hyperbolic systems Stability Morse-Smale Inducao Global Unfolding Inclination-flip Omega-limit sets 3-flows robustness partially hyperbolic conservative systems saddle-node arcs Physical measures dominated splitting Semi-dispersing billards Entropy expansiveness random perturbations non-conformal repellers cuspides nao compactas beta-expansao campos vetoriais planares Sistemas dinâmicos hitting time teorema de Denjoy atrator do tipo Lorenz taxa de mistura Rotation Multiplos de Divisao Robust Transitive Sets Partial hyperbolic entropy expnasive diffeomorphis decaimento lento resonant Contracting Lorenz-like attractor Rate of mixing ergodic bilhares dispersivos Rovella-like attractor Billiard with non compact cusps