Introduction to Dynamical Systems

By Andreas Knauf. 2003

906 citations recorded by the source corpus.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/94eb3bc947f399e99bd59f06ac697798ee1861f1

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Citations in the corpus

Birth of limit cycles bifurcating from a nonsmooth center (2014, background): “1 on page 20 of [1], is the following.”
The State of the Art in Flow Visualization: Dense and Texture‐Based Techniques (2004, neutral): “dynamical systems [1], given as set of differential equations).”
Physical measures and absolute continuity for one-dimensional center direction (2013, background): “Absolute continuity implies both lower and upper leafwise absolute continuity (see [15,16,23]); the converse is not true in general.”
Symbolic extensions for partially hyperbolic diffeomorphisms (2009, background): “Let M(f, X) be the set of invariant measures and Me(f, X) be the set of ergodic invariant measures for (X, f). If f is a homeomorphism of a compact metric space then M(f, X) is nonempty and satisfies the following (see [ 11, Section 4.6 ]): • M(f, X) is convex and compact for the weak∗-topology, and”
Stronger forms of sensitivity for dynamical systems (2007, background): “For example, for both the classes, (i) transitivity implies denseness of periodic points and (ii) total transitivity implies mixing (for subshifts of finite type, (ii) was observed in [21]; for the other results, see for instance, [8,9,23]).”
Dynamics of Network Selection in Heterogeneous Wireless Networks: An Evolutionary Game Approach (2009, methodology): “To obtain the solution to the differential equation corresponding to the replicator dynamics, we apply the Runge–Kutta method [23].”
Absolute continuity, Lyapunov exponents and rigidity I : geodesic flows (2011, background): “The converse is false: one can destroy absolute continuity of holonomy at a single transversal while keeping Lebesgue disintegration of volume (this is an exercise in Brin and Stuck [12]).”
Statistical inference for dynamical systems: A review (2012, background): “ergodic theory (for general references on dynamical systems and ergodic theory, see [10, 63, 97, 123]).”
Bifurcations in Nonsmooth Dynamical Systems (2008, background): “, [71, 4]) to describe bifurcations if the system is sufficiently smooth.”
Observability, Reconstructibility and State Observers of Boolean Control Networks (2013, methodology): “As a consequence of this algebraic set-up, logic-based problems can be converted into algebraic problems and hence solved by resorting to the standard mathematical tools available for linear state-space models and, in particular, for positive state-space models [10], [22], first of all graph theory.”
Simulated annealing and Boltzmann machines (2003, neutral): “Physical Review Letters, 58(9):913-916, March 1987.”