Progress in Nonlinear Science: Proceedings of the International Conference Dedicated to the 100th Anniversary of A. A. Andronov, Nizhny Novgorod, Russia, July 2-6, 2001. Mathematical problems of nonlinear dynamicsLev M. Lerman |
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analytic asymptotic attractor bi-asymptotic bifurcation billiard coefficients compute condition conjugate consider constant coordinates corresponding defined definition Denote diffeomorphism differential equations dimensional domain dynamical systems eigenvalues ellipsoid equilibrium exists finite fixed points formula function global Hamiltonian systems Hénon map heteroclinic cycle heteroclinic orbits homeomorphism homoclinic orbits hyperbolic infinite infinity integral intersection interval invariant manifolds Lemma limit cycles linear Lipschitz loop M₁ map F Math Mathematics matrix Moscow neighbourhood Nizhny Novgorod nonlinear normal form obtain oscillations parameter periodic orbits perturbation plane problem proof properties Proposition prove quadratic regions rescaled resonance return map rotation Russia e-mail saddle saddle-node satisfies separatrix simultaneous approximation singular point smooth solution stable and unstable surface symmetric model T₁ Theorem theory topological entropy torus trajectory transformation transversal two-dimensional unimodal map unstable manifolds values variables vector field zero