A continuous one-dimensional mapping without a measure with maximal entropy

1986 ◽  
Vol 20 (2) ◽  
pp. 134-136 ◽  
Author(s):  
B. M. Gurevich ◽  
A. S. Zargaryan
Keyword(s):  
Maximal Entropy ◽  
One Dimensional ◽  
Dimensional Mapping

scholarly journals On The Correlation between Properties of One-Dimensional Mappings of Control Functions and Chaos in a Special Type Delay Differential Equation

2017 ◽  
Vol 12 (2) ◽  
pp. 385-397 ◽  
Author(s):  
В.А. Лихошвай ◽  
V.A. Likhoshvai
Keyword(s):  
Differential Equation ◽  
Chaotic Dynamics ◽  
Molecular Genetic ◽  
Numerical Examples ◽  
One Dimensional ◽  
Control Functions ◽  
Delayed Argument ◽  
The One ◽  
Delay Differential ◽  
Dimensional Mapping

A differential equation of a special form, which contains two control functions f and g and one delayed argument, is analyzed. This equation has a wide application in biology for the description of dynamic processes in population, physiological, metabolic, molecular-genetic, and other applications. Specific numerical examples show the correlation between the properties of the one-dimensional mapping, which is generated by the ratio f /g, and the presence of chaotic dynamics for such equation. An empirical criterion is formulated that allows one to predict the presence of a chaotic potential for a given equation by the properties of the one-dimensional mapping f /g.

scholarly journals Diffusion and Superdiffusion from Hydrodynamic Projections

2022 ◽  
Vol 186 (2) ◽  
Author(s):  
Benjamin Doyon
Keyword(s):  
Lower Bounds ◽  
Hilbert Spaces ◽  
Fibonacci Sequence ◽  
Maximal Entropy ◽  
Many Body ◽  
One Dimensional ◽  
Covariant Derivatives ◽  
Many Body Systems ◽  
Nonlinear Fluctuating Hydrodynamics ◽  
Natural Expression

AbstractHydrodynamic projections, the projection onto conserved charges representing ballistic propagation of fluid waves, give exact transport results in many-body systems, such as the exact Drude weights. Focussing one one-dimensional systems, I show that this principle can be extended beyond the Euler scale, in particular to the diffusive and superdiffusive scales. By hydrodynamic reduction, Hilbert spaces of observables are constructed that generalise the standard space of conserved densities and describe the finer scales of hydrodynamics. The Green–Kubo formula for the Onsager matrix has a natural expression within the diffusive space. This space is associated with quadratically extensive charges, and projections onto any such charge give generic lower bounds for diffusion. In particular, bilinear expressions in linearly extensive charges lead to explicit diffusion lower bounds calculable from the thermodynamics, and applicable for instance to generic momentum-conserving one-dimensional systems. Bilinear charges are interpreted as covariant derivatives on the manifold of maximal entropy states, and represent the contribution to diffusion from scattering of ballistic waves. An analysis of fractionally extensive charges, combined with clustering properties from the superdiffusion phenomenology, gives lower bounds for superdiffusion exponents. These bounds reproduce the predictions of nonlinear fluctuating hydrodynamics, including the Kardar–Parisi–Zhang exponent 2/3 for sound-like modes, the Levy-distribution exponent 3/5 for heat-like modes, and the full Fibonacci sequence.

Deterministic hopping in a Josephson circuit described by a one-dimensional mapping

1985 ◽  
Vol 31 (4) ◽  
pp. 2509-2519 ◽  
Author(s):  
Robert F. Miracky ◽  
Michel H. Devoret ◽  
John Clarke
Keyword(s):  
One Dimensional ◽  
Dimensional Mapping

Error-detective one-dimensional mapping

2017 ◽  
Author(s):  
Yun Zhang ◽  
Shihao Zhou
Keyword(s):  
One Dimensional ◽  
Dimensional Mapping
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