One Dimensional Dynamics and The Rössler Attractor
One Dimensional Dynamics and The Rössler Attractor
The Rössler system is one of the best known chaotic dynamical systems, generating a chaotic attractor which, by the numerical evidence, arises by a period-doubling route to chaos. In this paper we state and prove a topological criterion for the existence of an attractor for the Rössler system - and then analyze the dynamics of the non-wandering set by reducing the flow to the dynamics of a well-known one dimensional model: the Quadratic Family, $x^2+c$, $-2\leq c\leq\frac{1}{4}$.
Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, FOS: Physical sciences, Dynamical Systems (math.DS), Mathematical Physics (math-ph), Mathematics - Dynamical Systems, Mathematical Physics
Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, FOS: Physical sciences, Dynamical Systems (math.DS), Mathematical Physics (math-ph), Mathematics - Dynamical Systems, Mathematical Physics
citations The total number of citations received by all articles of the researcher of interest.0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!