0000000001228614

AUTHOR

J Ros

showing 2 related works from this author

A fractal set from the binary reflected Gray code

2005

The permutation associated with the decimal expression of the binary reflected Gray code with $N$ bits is considered. Its cycle structure is studied. Considered as a set of points, its self-similarity is pointed out. As a fractal, it is shown to be the attractor of a IFS. For large values of $N$ the set is examined from the point of view of time series analysis

Discrete mathematicsPermutation (music)FísicaGeneral Physics and AstronomyBinary numberFOS: Physical sciencesStatistical and Nonlinear PhysicsNonlinear Sciences - Chaotic DynamicsDecimalGray codeSet (abstract data type)FractalAttractorPoint (geometry)Chaotic Dynamics (nlin.CD)Mathematical PhysicsMathematics
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Dynamics of a map with a power-law tail

2008

We analyze a one-dimensional piecewise continuous discrete model proposed originally in studies on population ecology. The map is composed of a linear part and a power-law decreasing piece, and has three parameters. The system presents both regular and chaotic behavior. We study numerically and, in part, analytically different bifurcation structures. Particularly interesting is the description of the abrupt transition order-to-chaos mediated by an attractor made of an infinite number of limit cycles with only a finite number of different periods. It is shown that the power-law piece in the map is at the origin of this type of bifurcation. The system exhibits interior crises and crisis-induc…

Statistics and ProbabilityMathematical analysisChaoticFOS: Physical sciencesGeneral Physics and AstronomyFísicaStatistical and Nonlinear PhysicsNonlinear Sciences - Chaotic DynamicsPower lawlaw.inventionNonlinear Sciences::Chaotic DynamicslawModeling and SimulationIntermittencyAttractorPiecewiseLimit (mathematics)Chaotic Dynamics (nlin.CD)Finite setMathematical PhysicsBifurcationMathematics
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