Transfer Operators with a Riesz Property

2018 ◽  
pp. 105-111
Author(s):  
Sergey Bezuglyi ◽  
Palle E. T. Jorgensen
Keyword(s):  
Transfer Operators ◽  
Riesz Property

scholarly journals On Gibbs Measures and Spectra of Ruelle Transfer Operators

2017 ◽  
Vol 60 (2) ◽  
pp. 411-421
Author(s):  
Luchezar Stoyanov
Keyword(s):  
Spectral Radius ◽  
Spectral Properties ◽  
Gibbs Measures ◽  
Transfer Operator ◽  
Frobenius Theorem ◽  
Transfer Operators

AbstractWe prove a comprehensive version of the Ruelle–Perron–Frobenius Theorem with explicit estimates of the spectral radius of the Ruelle transfer operator and various other quantities related to spectral properties of this operator. The novelty here is that the Hölder constant of the function generating the operator appears only polynomially, not exponentially as in previously known estimates.

scholarly journals SYNCHRONIZATION AS A PROCESS OF SHARING AND TRANSFERRING INFORMATION

2012 ◽  
Vol 22 (11) ◽  
pp. 1250261 ◽  
Author(s):  
ERIK M. BOLLT
Keyword(s):  
Symbolic Dynamics ◽  
Slow Manifold ◽  
Transfer Entropy ◽  
The Other ◽  
Chaotic Oscillators ◽  
Smale Horseshoe ◽  
Global System ◽  
Identity Function ◽  
Transfer Operators ◽  
First Time

Synchronization of chaotic oscillators has become well characterized by errors which shrink relative to a synchronization manifold. This manifold is the identity function in the case of identical systems, or some other slow manifold in the case of generalized synchronizaton in the case of nonidentical components. On the other hand, since many decades beginning with the Smale horseshoe, chaotic oscillators can be well understood in terms of symbolic dynamics as information producing processes. We study here the synchronization of a pair of chaotic oscillators as a process for sharing information bearing bits transferred between each other, by measuring the transfer entropy tracked as the global system transitions to the synchronization state. Further, we present for the first time the notion of transfer entropy in the measure theoretic setting of transfer operators.

scholarly journals Lattice reduction in two dimensions: analyses under realistic probabilistic models

2007 ◽  
Vol DMTCS Proceedings vol. AH,... (Proceedings) ◽  
Author(s):  
Brigitte Vallée ◽  
Antonio Vera
Keyword(s):  
Dynamical Systems ◽  
Probabilistic Models ◽  
Two Dimensions ◽  
Lattice Reduction ◽  
Lll Algorithm ◽  
Transfer Operators ◽  
International Audience ◽  
Dimension 2

International audience The Gaussian algorithm for lattice reduction in dimension 2 is precisely analysed under a class of realistic probabilistic models, which are of interest when applying the Gauss algorithm "inside'' the LLL algorithm. The proofs deal with the underlying dynamical systems and transfer operators. All the main parameters are studied: execution parameters which describe the behaviour of the algorithm itself as well as output parameters, which describe the geometry of reduced bases.

scholarly journals Pseudogenerators of Spatial Transfer Operators

2015 ◽  
Vol 14 (3) ◽  
pp. 1478-1517 ◽  
Author(s):  
Andreas Bittracher ◽  
Péter Koltai ◽  
Oliver Junge
Keyword(s):  
Transfer Operators
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