Y. Lacroix

• Agrégé 1989, PhD 1992, Habilitation Thesis 1997
• Professor (Full) 2000 at University of Toulon

The Bona beach, one of the beautiful sandy beaches along the eastern Giens double tombolo, is experiencing with severe coastal erosion which menaces its existence as well as many seaside properties on it. Submerged breakwaters (SBWs) are applied to this beach for the purpose of halting or at least limiting coastal erosion, stabilize the shoreline a...

Giens double tombolo linking Giens island to the mainland is a unique geomorphological formation in the world. However, its existence has been threatened by coastal erosion, especially in the eastern part of this tombolo. The investigation of historical shoreline changes along the eastern Giens tombolo were carried out applying the integration of s...

In this study, the remote sensing and Geographic Information System (GIS) techniques coupled with the Digital Shoreline Analysis System (DSAS) is applied to detect the historical shoreline changes as well as to predict the future shoreline position along Almanarre beach which is being threatened by severe erosion. The results show that Almanarre be...

The Ceinturon beach in the eastern Giens tombolo has been eroded since 1970s. Beach nourishment has already been applied to recover it. In this paper, the effects of beach nourishment on hydrodynamics and sediment transport of Ceinturon beach are investigated by using the numerical models. These numerical models were calibrated with field data. All...

Rising sea level along with the occurrence of greater and more frequent storms would cause not only coastal flooding, but also beach erosion and shoreline retreat problems. The Almanarre beach along the western Giens tombolo is socio-economically and heavily vulnerable to accelerated sea level rise due to its high touristic value and low-lying topo...

Beaches along the eastern branch of the Giens double tombolo are subject to coastal erosion. Prediction of the behavior of the beach profile configuration in response to natural and anthropogenic changes using the concept of equilibrium beach profile (EBP) could be useful in finding the most suitable measure to address the erosion problem. Field in...

Posidonia oceanica plays a significant role in the stabilization and protection of the coast in Gulf of Giens. Unfortunately, its distribution has been declining remarkably due to both anthropogenic interventions and natural factors. The present study focuses on the numerical simulation of the presence of Posidonia as well as the influence of its d...

The present study aims to utilize the combination of remote sensing and Geographic Information System (GIS) techniques coupled with the Digital Shoreline Analysis System (DSAS) to investigate the historical shoreline changes as well as to predict the position of future shoreline in Almanarre beach which is being threatened by erosion. The results i...

The Almanarre Beach in Toulon is submitted to shoreline erosion. We use statistical methods from Digital Shoreline Analysis System in order to better understand the historical and future shoreline changes. The End Point Rate method is used to estimate the shoreline change rates. The results show the annual shoreline change rates for four sectors of...

The nice and attractive beach located south of La Capte port is subject to coastal erosion. It gradually disappears under the impact of waves and storms, especially in the autumn and winter. To limit this erosion, geotextile submerged breakwaters were established in February-March 2008 accompanying beach nourishment. The implementation of these sub...

The western Tombolo of the Giens peninsula in southern France, known as Almanarre beach, is subject to coastal erosion. We are trying to use computer simulation in order to propose solutions to stop this erosion. Our aim was first to determine the main factors for this erosion and successfully apply a coupled hydro-sedimentological numerical model...

The tombolo of Giens is located in the town of Hyères (France). We recall the history of coastal erosion, and prominent factors affecting the evolution of the western tombolo. We then discuss the possibility of stabilizing the western tombolo. Our argumentation relies on a coupled model integrating swells, currents, water levels and sediment transp...

The tombolo of Giens is located in the town of Hyères (France). We recall the history of coastal erosion, and prominent factors affecting the evolution of the western tombolo. We then discuss the possibility of stabilizing the western tombolo. Our argumentation relies on a coupled model integrating swells, currents, water levels and sediment transp...

We define new isomorphism invariants for ergodic measure-preserving systems on standard probability spaces, called measure-theoretic chaos and measure-theoretic+ chaos. These notions are analogs of the topological chaos DC2 and its slightly stronger version (which we denote by DC1 1/2). We prove that: (1) if a topological system is measure-theoreti...

After surveying the known connections between topological entropy zero and nonexistence of certain types of pairs in the system, we supplement them by showing that a topological dynamical system has topological entropy zero if and only if it is a factor of a system with no forward mean asymptotic pairs. This covers two former statements of [D. Orns...

Let T be a continuous map on a compact metric space (X, d). A pair of distinct points x, y ∈ X is asymptotic if lim n→∞ d(T n x, T n y) = 0. We prove the following four conditions to be equivalent: 1. h top(T) = 0; 2. (X, T) has a (topological) extension (Y,S) which has no asymptotic pairs; 3. (X, T) has a topological extension (Y ′, S′) via a...

Characteristics of light wave propagating in a turbulent sea water are determined by fluctuation spectrum of optical refractive index n. The behavior of the spectrum is controlled by fluctuations of temperature and salinity. Acoustic scattering from oceanic microstructure is due to sound speed and density fluctuations that in turn also depend on th...

Attracting and repelling are discussed on two levels: in abstract signal processes and in signal processes arising as returns to a fixed set in an ergodic dy-namical system. In the first approach, among other things, we give three examples in which the sum of two Poisson (hence neutral – neither attracting nor repelling) pro-cesses comes out either...

This volume contains a selection from the contributions to the School in ergodic theory, housed at CIRM (Marseilles, France) during April 2006. This edition involves several themes. Dynamical properties of interval maps are studied in case of unimodal transformations and piecewise monotonic maps, but also for generalized -shift and some Gibbs prope...

This article deals with a study case which models the officer behavior in a submarine, and more especially in a case of an adversary detection. This application has been implemented in Prolog. Naval action's simulations estimate the operational performance of warships or submarines for a given scenario. In common models, the operator's reactions ar...

In a stationary ergodic process, clustering is defined as the tendency of events to appear in series of increased frequency separated by longer breaks. Such behavior, contradicting the theoretical "unbiased behavior" with exponential distribution of the gaps between appearances, is commonly observed in experimental processes and often difficult to...

We consider an ergodic process on finitely many states, with positive entropy. Our first main result asserts that the distribution function of the normalized waiting time for the first visit to a small (i.e., over a long block) cylinder set $B$ is, for majority of such cylinders and up to epsilon, dominated by the exponential distribution function...

We prove a general ergodic-theoretic result concerning the return time statistic, which, properly understood, sheds some new light on the common sense phenomenon known as the law of series. Let (P Z , µ, σ) be an ergodic process on finitely many states, with positive entropy. We show that the distribution function of the normalized waiting time for...

In this paper we characterize possible asymptotics for hitting times in aperiodic ergodic dynamical systems: asymptotics are proved to be the distribution functions of subprobability measures on the line belonging to the functional class {6pt} {-3mm}(A){6mm}F={F:R\to [0,1]:\left\lbrack \matrixF is increasing, null on ]-\infty, 0]; \noalignF is cont...

Given an ergodic dynamical system $(X,T,\mu)$, and $U\subset X$ measurable with $\mu (U)>0$, let $\mu (U)\tau_U(x)$ denote the normalized hitting time of $x\in X$ to $U$. We prove that given a sequence $(U_n)$ with $\mu (U_n)\to 0$, the distribution function of the normalized hitting times to $U_n$ converges weakly to some sub-probability distribut...

We construct infinite dimensional chains that are ℒ1 good for almost sure convergence, which settles a question raised in this journal [7] and earlier in [6] by R. Nair. In [7] it was stated that the construction proposed in [4] was invalid. We complete the construction proposed in [4], where it is true that a piece of proof was forgotten. The tech...

We introduce a new class of cocycles which provides examples of measure preserving dynamical systems (X,B,μ,T), such that given positive integers r≥2 and m≥1, possibly infinite, with (r,m)≠(∞,∞), the rank is r and the order of the quotient group in the measure-theoretic centralizer, #C(T) wcl {T n ,n∈ℤ}, is m. Moreover, wcl {T n ,n∈ℤ} is uncountabl...

LetG denote the set of decreasingG: ℝ→ℝ withGэ1 on ]−∞,0], and ƒ 0 ∞ G(t)dt⩽1. LetX be a compact metric space, andT: X→X a continuous map. Let μ denone aT-invariant ergodic probability measure onX, and assume (X, T, μ) to be aperiodic. LetU⊂X be such that μ(U)>0. Let τ U (x)=inf{k⩾1:T k xεU}, and defineG U (t)=1/u(U)u({xεU:u(U)τU(x)>t),tεℝ We p...

. We introduce the notion of local perturbations for normalized energies and study their e#ect on the level of equilibrium measures. Using coupling technics and Kac's return time theorem, we obtain some d-estimates for the equilibrium measures. These reveal stability of certain energies under local perturbations. They also show how some weak-# conv...

. We observe that the standard Kemeny and Snell identity, basic in Markov Chain Perturbation Theory, generalizes to chains with complete connections. Therefrom a few elementary observations are derived for weak-perturbation of g-measures considered as a function of g. This identity is applied to produce a simple proof for the phase transition pheno...

A combinatorial,description,of spectral isomorphisms,between,Morse flows is provided. We introduce,the notion of a regular spectral isomorphism,and we study some invariants of such isomorphisms. In the case of Morse cocycles taking values in G = Zp, wherep is a prime, each spectral isomorphism is regular. The same holds true for arbitrary finite ab...

We show that Turyn's conjecture, arising from the Theory of Error Cor- recting Codes, has an equivalent formulation in Dynamical Systems Theory. In par- ticular, Turyn's conjecture is true if all binary Morse ∞ows have singular spectra. Our proof uses intermediate estimates for merit factors of products of words, and is purely combinatorial. Resume...

Let (Z, TZ) be a minimal non-periodic flow which is either symbolic or strictly ergodic. Any topological extension of (Z, TZ) is Borel isomorphic to an almost 1-1 extension of (Z, TZ). Moreover, this isomorphism preserves the affine-topoogical structure of the invariant measures. The above extends a theorem of Furstenberg-Weiss (1989). As an applic...

For any pair(m, r) such that2 ≤ m ≤ r > ∞, we construct an ergodic dynamical system having spectral multiplicitym and rankr. The essential range of the multiplicity function is described. Ifr ≥ 2, the pair(m, r) also has a weakly mixing realization.

Given an arbitrary countable subgroup σ o of the torus, containing in-finitely many rationals, we construct a strictly ergodic 0-1 Toeplitz flow with pure point spectrum equal to σ o . For a large class of Toeplitz flows certain eigenvalues are induced by eigenvalues of the flow Y which can be seen along the aperiodic parts.

Given a number system T = (0, 1), T(j), (J(n, j)n is-an-element-of E(j))j greater-than-or-equal-to 0, we define a measurable mapping PHI(T): (0, 1)N --> (0, 1) such that lambda(infinity) (PHI(T)-1(A)) = lambda(A), A is-an-element-of B(0, 1). A measurable section (t(n)(.))n greater-than-or-equal-to 0 is defined for PHI(T); t(n)(.) has uniform distri...

The maximal zero entropy factor of a topological flow is defined using entropy pairs and explicitly given for some simple cartesian products. As a consequence, it is proved that only the trivial flow is disjoint from all flows whose maximal zero entropy factor is trivial.

Simulations of naval action estimate the operational performance of warships or submarines for a given scenario. In common models, the operator’s reactions are predefined. This is not realistic: the operator’s decision can produce unexpected reactions. This paper presents a method to model operator decision in simulations. This method allows to re...