scholarly journals The Dual Potential, the Involution Kernel and Transport in Ergodic Optimization

2015 ◽  
pp. 357-398 ◽  
Author(s):  
A. O. Lopes ◽  
E. R. Oliveira ◽  
Ph. Thieullen
Keyword(s):  
Ergodic Optimization

scholarly journals Ergodic Optimization for Renewal Type Shifts

2006 ◽  
Vol 150 (2) ◽  
pp. 91-95 ◽  
Author(s):  
Godofredo Iommi
Keyword(s):  
Ergodic Optimization

Ergodic optimization for noncompact dynamical systems

2007 ◽  
Vol 22 (3) ◽  
pp. 379-388 ◽  
Author(s):  
O. Jenkinson ◽  
R. D. Mauldin ◽  
M. Urbański
Keyword(s):  
Dynamical Systems ◽  
Ergodic Optimization

scholarly journals Optimization of Energy Storage Operation Chart of Cascade Reservoirs with Multi-Year Regulating Reservoir

Energies ◽  
2019 ◽  
Vol 12 (20) ◽  
pp. 3814 ◽  
Author(s):  
Yi Liu ◽  
Zhiqiang Jiang ◽  
Zhongkai Feng ◽  
Yuyun Chen ◽  
Hairong Zhang ◽  
...  
Keyword(s):  
Energy Storage ◽  
Optimization Model ◽  
Total Power ◽  
Cascade Reservoirs ◽  
Optimal Output ◽  
Ergodic Optimization ◽  
Cascade Energy ◽  
Actual Operation ◽  
Innovative Work ◽  
The Difference

In view of the problems that have not been solved or studied in the previous studies of cascade Energy Storage Operation Chart (ESOC), based on a brief description of the composition, principle, drawing methods, and simulation methods of ESOC, the following innovative work has been done in this paper. Firstly, considering the inconsistency of inflow frequency of upstream and downstream watershed in selecting the typical dry years, a novel optimization model for selecting the overall inflow process considering the integrity of watershed was proposed, which aimed at minimizing the sum of squares of inflow frequency differences. Secondly, aiming at the influence of output coefficients (including number and values) on the results of ESOC, this paper proposed a new method to construct the initial solution of output coefficients and established an optimization model of output coefficients based on progressive optimality algorithms. Thirdly, to the optimization of ESOC with multi-year regulating reservoir, a discrete optimization model of drawdown level was constructed based on the idea of ergodic optimization. On these bases, taking the seven reservoirs in the Yalong River basin of China as an example, the typical dry years considering the inflow frequency inconsistency, the optimal output coefficients of ESOC and the optimal end-of-year drawdown level of a multi-year regulating reservoir (Lianghekou) were obtained, and compared with the previous research results, the ESOC optimized in this paper can increase the total power generation of the cascade system by 9% under the condition that the guaranteed rate did not change much. Furthermore, the difference of the optimal end-of-year drawdown levels between the cascade joint operation and single reservoir operation was discussed for the Lianghekou reservoir at the end of the case study. The obtained results were of great significance for guiding the actual operation of cascade reservoirs.

scholarly journals Ergodic optimization in dynamical systems

2018 ◽  
Vol 39 (10) ◽  
pp. 2593-2618 ◽  
Author(s):  
OLIVER JENKINSON
Keyword(s):  
Probability Measure ◽  
Invariant Measures ◽  
Model Problem ◽  
Thermodynamic Formalism ◽  
Invariant Probability Measure ◽  
Temperature Limit ◽  
Zero Temperature ◽  
Ergodic Optimization ◽  
Maximizing Measure ◽  
Time Average

Ergodic optimization is the study of problems relating to maximizing orbits and invariant measures, and maximum ergodic averages. An orbit of a dynamical system is called$f$-maximizing if the time average of the real-valued function$f$along the orbit is larger than along all other orbits, and an invariant probability measure is called$f$-maximizing if it gives$f$a larger space average than any other invariant probability measure. In this paper, we consider the main strands of ergodic optimization, beginning with an influential model problem, and the interpretation of ergodic optimization as the zero temperature limit of thermodynamic formalism. We describe typical properties of maximizing measures for various spaces of functions, the key tool of adding a coboundary so as to reveal properties of these measures, as well as certain classes of functions where the maximizing measure is known to be Sturmian.

scholarly journals Ergodic Optimization for Hyperbolic Flows and Lorenz Attractors

2020 ◽  
Vol 21 (10) ◽  
pp. 3253-3283 ◽  
Author(s):  
Marcus Morro ◽  
Roberto Sant’Anna ◽  
Paulo Varandas
Keyword(s):  
Ergodic Optimization ◽  
Hyperbolic Flows ◽  
Lorenz Attractors

Aubry set for asymptotically sub-additive potentials

2016 ◽  
Vol 16 (02) ◽  
pp. 1660009 ◽  
Author(s):  
Eduardo Garibaldi ◽  
João Tiago Assunção Gomes
Keyword(s):  
Dynamical Systems ◽  
Spectral Radius ◽  
Sufficient Conditions ◽  
Optimization Theory ◽  
Joint Spectral Radius ◽  
Maximum Value ◽  
Ergodic Optimization ◽  
Aubry Set ◽  
Central Result ◽  
Topological Dynamical Systems

Given a topological dynamical systems [Formula: see text], consider a sequence of continuous potentials [Formula: see text] that is asymptotically approached by sub-additive families. In a generalized version of ergodic optimization theory, one is interested in describing the set [Formula: see text] of [Formula: see text]-invariant probabilities that attain the following maximum value [Formula: see text] For this purpose, we extend the notion of Aubry set, denoted by [Formula: see text]. Our central result provides sufficient conditions for the Aubry set to be a maximizing set, i.e. [Formula: see text] belongs to [Formula: see text] if, and only if, its support lies on [Formula: see text]. Furthermore, we apply this result to the study of the joint spectral radius in order to show the existence of periodic matrix configurations approaching this value.

scholarly journals Ergodic optimization for countable alphabet subshifts of finite type

2006 ◽  
Vol 26 (06) ◽  
pp. 1791 ◽  
Author(s):  
O. JENKINSON ◽  
R. D. MAULDIN ◽  
M. URBANSKI
Keyword(s):  
Finite Type ◽  
Ergodic Optimization ◽  
Subshifts Of Finite Type

scholarly journals Ergodic Optimization of Prevalent Super-continuous Functions

2015 ◽  
Vol 2016 (19) ◽  
pp. 5988-6017 ◽  
Author(s):  
Jairo Bochi ◽  
Yiwei Zhang
Keyword(s):  
Continuous Functions ◽  
Ergodic Optimization
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