Related papers: Ergodic Optimization of Super-continuous Functions…
Ergodic optimization aims to single out dynamically invariant Borel probability measures which maximize the integral of a given "performance" function. For a continuous self-map of a compact metric space and a dense set of continuous…
Ergodic optimization aims to describe dynamically invariant probability measures that maximize the integral of a given function. For a wide class of intrinsically ergodic subshifts over a finite alphabet, we show that the space of…
Ergodic optimization is the study of problems relating to maximizing orbits, maximizing 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…
Ergodic optimization aims to describe dynamically invariant probability measures that maximize the integral of a given function. The Dyck and Motzkin shifts are well-known examples of transitive subshifts over a finite alphabet that are not…
We study the optimization of ergodic averages for multi-valued dynamical systems, i.e. where points may have multiple different forward orbits. Under upper semi-continuity assumptions, we show that the maximum space average with respect to…
The theory of ergodic optimization for distance-expanding maps is extended to Gauss's continued fraction map. Since the set of invariant probability measures is not weak$^*$ closed, we establish a characterisation of the closure of this…
We study the ergodic optimization problem over a real analytic expanding circle map. We show that in both the topological and the measure-theoretical senses, a typical $C^r$ performance function has a unique maximizing measure and the…
Given a dynamical system, we say that a performance function has property P if its time averages along orbits are maximized at a periodic orbit. It is conjectured by several authors that for sufficiently hyperbolic dynamical systems,…
In search and surveillance applications in robotics, it is intuitive to spatially distribute robot trajectories with respect to the probability of locating targets in the domain. Ergodic coverage is one such approach to trajectory planning…
In this article, we pay attention to transitive dynamical systems having the shadowing property and the entropy functions are upper semicontinuous. As for these dynamical systems, when we consider ergodic optimization restricted on the…
One of the fundamental results of ergodic optimization asserts that for any dynamical system on a compact metric space with the specification property and for a generic continuous function $f$ every invariant probability measure that…
For ergodic optimization on any topological dynamical system, with real-valued potential function $f$ belonging to any separable Banach space $B$ of continuous functions, we show that the $f$-maximizing measure is typically unique, in the…
Ergodic control synthesizes optimal coverage behaviors over spatial distributions for nonlinear systems. However, existing formulations model the robot as a non-volumetric point, whereas in practice a robot interacts with the environment…
One of the fundamental results of ergodic optimisation asserts that for any dynamical system on a compact metric space $X$ and for any Banach space of continuous real-valued functions on $X$ which embeds densely in $C(X)$ there exists a…
In this paper, we study ergodic optimization of continuous functions for flows by concentrating on the entropy spectrum of their maximizing measures. Precisely, over a wide family of flows with non-uniformly hyperbolic structure, we obtain…
In this work, we show the consistency of an approach for solving robust optimization problems using sequences of sub-problems generated by ergodic measure preserving transformations. The main result of this paper is that the minimizers and…
This paper addresses the problem of trajectory planning for information gathering with a dynamic and resolution-varying sensor footprint. Ergodic planning offers a principled framework that balances exploration (visiting all areas) and…
We extend the theory of ergodic optimization and maximizing measures to the non-commutative field of C*-dynamical systems. We then provide a result linking the ergodic optimizations of elements of a C*-dynamical system to the convergence of…
We present a novel formulation of ergodic trajectory optimization that can be specified over general domains using kernel maximum mean discrepancy. Ergodic trajectory optimization is an effective approach that generates coverage paths for…
In this paper The Ergodic Hypothesis is proven for one class of functions defined in the infinite dimensional unite cube where is given an action of some semigroup of mappings without the condition on metric transitivity. The result has not…