Structures in dynamics: finite dimensional deterministic studies
The study of non-linear dynamical systems nowadays is an intricate mixture of analysis, geometry, algebra and measure theory and this book takes all aspects into account. Presenting the contents of its authors' graduate courses in non-linear dynamical systems, this volume aims at researchers who wish to be acquainted with the more theoretical and fundamental subjects in non-linear dynamics and is designed to link the popular literature with research papers and monographs. All of the subjects covered in this book are extensively dealt with and presented in a pedagogic form. These include the presentation of an environment for the route to chaos by quasi-periodicity (which is related to the Landau-Lifschitz and Ruelle-Takens scenario's concerning the onset of turbulence); the theories of 1-dimensional dynamics, singularities in planar vector fields, and quasi-periodicity in dissipative systems.
15 pages matching period doubling in this book
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Introduction to dynamical systems if W Broer
Genericity and structural stability
Bifurcations F Takens
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1-parameter family action-angle variables asymptotic basin behaviour blowing-up Bogdanov-Takens bifurcation C°-equivalence called Cantor set centre manifold closed orbit codimension compact compare Chapter conjugacy consider contains coordinates corresponding curves defined definition denote diffeomorphisms differential equations dynamical systems eigenvalues entropy equivalent ergodic measures example exists Figure fixed point follows given Hamilton function Hamiltonian Hamiltonian vector field homeomorphism homterval Hopf bifurcation hyperbolic implies integrable invariant measures iterates Jacobian Lebesgue measure lemma linear Math negative Schwarzian derivative neighbourhood Normal Form parameter pendulum period doubling periodic attractor periodic orbit periodic point perturbation phase portrait phase space Poincare mapping point attractor probability measure proof quadratic quasi-periodic resp restrict Ruelle saddle node bifurcation Schwarzian derivative sensitive dependence sequence singularities Springer-Verlag stationary structurally stable Subsection symplectic Theorem theory topological torus turning point Twist Mapping unstable manifolds vector fields versal unfolding wandering interval yd/dx zero