Minimal Periodic Orbit Structure of 2-Dimensional Homeomorphisms

Solari, Hernán G.; Natiello, Mario A.

doi:10.1007/s00332-005-0637-1

Cited by 4 publications

(3 citation statements)

References 12 publications

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“…However, it is very difficult to find the location of periodic orbits and the Markov partition from experimental pictures. In contrast, for the map, the partition can be determined by partitioning the unit interval using the iterates of periodic points [61].…”

Section: Symbolic Dynamics Of the Open-flow Baker's Mapmentioning

confidence: 99%

Open-flow mixing: Experimental evidence for strange eigenmodes

et al. 2009

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We investigate experimentally the mixing dynamics of a blob of dye in a channel flow with a finite stirring region undergoing chaotic advection. We study the homogenization of dye in two variants of an eggbeater stirring protocol that differ in the extent of their mixing region. In the first case, the mixing region is separated from the side walls of the channel, while in the second it extends to the walls. For the first case, we observe the onset of a permanent concentration pattern that repeats over time with decaying intensity. A quantitative analysis of the concentration field of dye confirms the convergence to a self-similar pattern, akin to the strange eigenmodes previously observed in closed flows. We model this phenomenon using an idealized map, where an analysis of the mixing dynamics explains the convergence to an eigenmode. In contrast, for the second case the presence of no-slip walls and separation points on the frontier of the mixing region leads to non-self-similar mixing dynamics.

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Section: Symbolic Dynamics Of the Open-flow Baker's Mapmentioning

confidence: 99%

Open-flow mixing: Experimental evidence for strange eigenmodes

et al. 2009

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“…Every of these thick maps can be reduced using methods to determine its minimal representative, e.g. [1,5].…”

Section: Forcing Of Renormalizable Orbitsmentioning

confidence: 99%

Renormalization and forcing of horseshoe orbits

Mendoza

2014

Topology and its Applications

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“…The restrictions determined by the 3-dimensional phase-space impose a rigid structure to the periodic orbits of the oscillator for any given parameter value. This structure, a 3-dimensional analogue of Sarkovskii's order [5,6], encapsulates in the form of braids much of the information of the chaotic sets of forced oscillators [7,8,9,10,11,12,13,14,15].…”

Section: Introductionmentioning

confidence: 99%