The Lyapunov spectrum of a stochastic flow of diffeomorphisms

1986 ◽  
pp. 322-337 ◽  
Author(s):  
Peter H. Baxendale
Keyword(s):  
Lyapunov Spectrum ◽  
Stochastic Flow ◽  
Stochastic Flow Of Diffeomorphisms

LYAPUNOV SPECTRUM OF NONAUTONOMOUS LINEAR STOCHASTIC DIFFERENTIAL ALGEBRAIC EQUATIONS OF INDEX-1

2012 ◽  
Vol 12 (04) ◽  
pp. 1250002 ◽  
Author(s):  
NGUYEN DINH CONG ◽  
NGUYEN THI THE
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Lyapunov Exponents ◽  
Algebraic Equation ◽  
Differential Algebraic Equations ◽  
Lyapunov Spectrum ◽  
Stochastic Flow ◽  
Algebraic Equations ◽  
Differential Algebraic Equation ◽  
Two Parameter

We introduce a concept of Lyapunov exponents and Lyapunov spectrum of a stochastic differential algebraic equation (SDAE) of index-1. The Lyapunov exponents are defined samplewise via the induced two-parameter stochastic flow generated by inherent regular stochastic differential equations. We prove that Lyapunov exponents are nonrandom.

scholarly journals Lyapunov spectrum of a relativistic stochastic flow in the Poincaré group

2014 ◽  
Vol 14 (04) ◽  
pp. 1450013 ◽  
Author(s):  
Camille Tardif
Keyword(s):  
Lyapunov Spectrum ◽  
Stochastic Flow ◽  
Stochastic Flows ◽  
Poincaré Group ◽  
Stable Manifolds ◽  
Poincare Group ◽  
Relativistic Processes

We determine the Lyapunov spectrum and stable manifolds of some stochastic flows on the Poincaré group associated to Dudley's relativistic processes.

scholarly journals How Many Inflections are There in the Lyapunov Spectrum?

2021 ◽  
Author(s):  
O. Jenkinson ◽  
M. Pollicott ◽  
P. Vytnova
Keyword(s):  
Piecewise Linear ◽  
Lyapunov Spectrum ◽  
Stat Phys ◽  
Linear Map ◽  
Piecewise Linear Map ◽  
Expanding Map ◽  
Lyapunov Spectra ◽  
Linear Maps ◽  
Inflection Points ◽  
Piecewise Linear Maps

AbstractIommi and Kiwi (J Stat Phys 135:535–546, 2009) showed that the Lyapunov spectrum of an expanding map need not be concave, and posed various problems concerning the possible number of inflection points. In this paper we answer a conjecture in Iommi and Kiwi (2009) by proving that the Lyapunov spectrum of a two branch piecewise linear map has at most two points of inflection. We then answer a question in Iommi and Kiwi (2009) by proving that there exist finite branch piecewise linear maps whose Lyapunov spectra have arbitrarily many points of inflection. This approach is used to exhibit a countable branch piecewise linear map whose Lyapunov spectrum has infinitely many points of inflection.

Buffer allocation in stochastic flow lines via sample-based optimization with initial bounds

OR Spectrum ◽  
2015 ◽  
Vol 37 (4) ◽  
pp. 869-902 ◽  
Author(s):  
Sophie Weiss ◽  
Raik Stolletz
Keyword(s):  
Stochastic Flow ◽  
Buffer Allocation ◽  
Flow Lines

scholarly journals Lyapunov spectrum of ball quotients with applications to commensurability questions

2016 ◽  
Vol 165 (1) ◽  
pp. 1-66 ◽  
Author(s):  
André Kappes ◽  
Martin Möller
Keyword(s):  
Lyapunov Spectrum ◽  
Ball Quotients
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