birational automorphism groups and the movable cone theorem for calabi yau manifolds of wehler type via universal coxeter groups thanks to the theory of coxeter groups we produce the first family of calabi yau manifolds x of arbitrary dimension n for which rm bir x is infinite and the kawamata morrison movable cone conjecture is satisfied for this family the movable cone is explicitly described it s fractal nature is related to limit sets of kleinian groups and to the apollonian gasket then we produce explicit examples of biregular automorphisms with positive entropy on some calabi yau varieties

an ergodic study of painleve vi an ergodic study of painleve vi is developed the chaotic nature of its poincare return map is established for almost all loops the exponential growth of the numbers of periodic solutions is also shown principal ingredients of the arguments are a moduli theoretical formulation of painleve vi a riemann hilbert correspondence the dynamical system of a birational map on a cubic surface and the lefschetz fixed point formula

automorphisms of compact kahler manifolds with slow dynamics we study the automorphisms of compact k ahler manifolds having slow dynamics by adapting gromov s classical argument we give an upper bound on the polynomial entropy and study its possible values in dimensions 2 and 3 we prove that every automorphism with sublinear derivative growth is an isometry a counter example is given in the c infty context answering negatively a question of artigue carrasco olivera and monteverde on polynomial entropy finally we classify minimal automorphisms in dimension 2 and prove they exist only on tori we conjecture that this is true for any dimension

dynamics of rational surface automorphisms rotation domains a fatou component is said to be a rotation domain if the automorphism induces a torus action on it we construct a rational surface automorphism with positive entropy and a rotation domain which contains both a curve of fixed points and isolated fixed points this fatou component cannot be imbedded into complex euclidean space so we introduce a global linear model space and show that it can be globally linearized in this model

statistical properties of chaotic systems the theory of smooth dynamical systems and the theory of abstract dynamical systems ergodic theory although having the same roots have for many years developed quite independently of one another these theories have now matured to the point where they can be combined to shed light on the nature of chaotic behavior

green currents for holomorphic automorphisms of compact kahler manifolds and some additional regularity properties very likely the currents t will describe the distribution of invariant manifolds of codimension s corresponding to the small est lyapounov exponents let dp denote the dynamical degree of order p of it describes the growth under iteration of the volume of p dimensional manifolds when d 1 it is natural to introduce first a positive closed 1 l current as ifnyoj 7 lim

post critical set and non existence of preserved meromorphic 2 forms we present a family of birational transformations in cp2 depending on two or three parameters which do not generically preserve meromorphic 2 forms with the introduction of the orbit of the critical set vanishing condition of the jacobian also called the post critical set we get some new structures some non analytic 2 form which reduce to meromorphic 2 forms for particular subvarieties in the parameter space on these subvarieties the iterates of the critical set have a polynomial growth in the degrees of the parameters while one has an exponential growth out of these subspaces the analysis of our birational transformation in cp2 is first carried out using the diller favre criterion in order to find the complexity reduction of the mapping the integrable cases are found the identification between the complexity growth and the topological entropy is once again verified we perform plots of the post critical set as well as calculations of lyapunov exponents for many orbits confirming that generically no meromorphic 2 form can be preserved for this mapping these birational transformations in cp2 which generically do not preserve any meromorphic 2 form are extremely similar to other birational transformations we previously studied which do preserve meromorphic 2 forms we note that these two sets of birational transformations exhibit totally similar results as far as topological complexity is concerned but drastically different results as far as a more probabilistic approach of dynamical systems is concerned lyapunov exponents with these examples we see that the existence of a preserved meromorphic 2 form explains most of the numerical discrepancies between the topological and probabilistic approaches of dynamical systems

rational surfaces with a large group of automorphisms we classify rational surfaces for which the image of the automorphisms group in the group of linear transformations of the picard group is the largest possible this answers a question raised by arthur coble in 1928 and can be rephrased in terms of periodic orbits of a birational action of an infinite coxeter group on ordered point sets in the projective plane modulo projective equivalence we also outline the classification of non rational surfaces with large automorphism groups

energy and invariant measures for birational surface maps given a birational self map of a compact complex surface it is useful to find an invariant measure that relates the dynamics of the map to its action on cohomology under a very weak hypothesis on the map we show how to construct such a measure the main point in the construction is to make sense of the wedge product of two positive closed 1 1 currents we are able to do this in our case because local potentials for each current have finite energy with respect to the other our methods also suffice to show that the resulting measure is mixing does not charge curves and has nonzero lyapunov exponents

dynamics of automorphisms on compact kahler manifolds we study holomorphic automorphisms on compact kahler manifolds having simple actions on the hodge cohomology ring we show for such automorphisms that the main dynamical green currents admit complex laminar structures woven currents and the green measure is the unique invariant probability measure of maximal entropy

observers and parameter determination for distributed parameter systems the aim of the paper is to investigate the estimation of unknown states and unknown functions for distributed parameter systems first we construct finite dimensional state observers to estimate the unknown states and give the error estimates for the distributed parameter systems of parabolic type with unknown input sources next we consider the determination of unknown input distribution functions using these estimated states the problems of unknown function determination are not necessarily well posed even if the distributed parameter systems are identifiable a well posed approximation method by regularization is applied to obtain the approximate functions which depend continuously on the measurement data we also construct finite dimensional state observers for the distributed parameter systems of hyperbolic type with unknown input sources simple numerical examples are presented

dynamics of bimeromorphic maps of surfaces we classify bimeromorphic self maps f x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i of compact kahler surfaces x in terms of their actions f h 1 1 x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i on cohomology we observe that the growth rate of f n is invariant under bimeromorphic conjugacy and that by conjugating one can always arrange that f n f n we show that the sequence f n can be bounded grow linearly grow quadratically or grow exponentially in the first three cases we show that after conjugating f is an automorphism virtually isotopic to the identity f preserves a rational fibration or f preserves an elliptic fibration respectively in the last case we show that there is a unique up to scaling expanding eigenvector for f that is nef and that f is bimeromorphically conjugate to an automorphism if and only if 2 0 we go on in this case to construct a dynamically natural positive current representing and we study the growth rate of periodic orbits of f we conclude by illustrating our results with a particular family of examples

necessary condition on the dissipative term for the asymptotically free property of dissipative kirchhoff equations abstract it is known that the solutions of linear abstract dissipative wave equation with integrable coefficient of the dissipation term are asymptotically free namely the solutions have the same asymptotic behavior as that of the solutions of an abstract free wave equation in this paper we conclude that the integrability is not enough for asymptotic free property of kirchhoff equation by showing the following for the existence of a non trivial asymptotically free solution of abstract kirchhoff equation with initial data in some class an essentially stronger decay condition on the coefficient of dissipation term is necessary

sur les groupes de transformations birationnelles des surfaces ni agissant par transformations bi rationnelles sur les surfaces complexes compactes kahl eriennes nous mon trons a que le groupe des transformations birationnelles d une surface satisfait l alternative de tits b que les actions birationnelles de groupes de kazhdan sur les surfaces sont toutes birationnellement conjugu eesa des actions homographiques sur le plan projectif et c que si f et g sont deux transformations birationnelles de surfaces qui commutent alors ou bien f pr eserve un pinceau de courbes ou bien l un des it er es g m de g m 0 concide avec un it er e f n de f n 2 z let s be any compact complex kahler surface and bir s the group of birational transformations of s we study the structure of nitely genera ted subgroups of bir s and prove three main results a bir s satises the tits alternative b if a group with kazhdan property t acts on a compact kahler surface by birational transformations then the action is conjugate to an action by linear projective transformations on the projec tive plane and c if f is an element of bir s which does not preserve any pencil of curves and if g commutes with f then a positive iterate of g coincides with an iterate of f the second statement provides a positive answer to zimmer s conjecture for birational actions on surfaces

constraints on automorphism groups of higher dimensional manifolds abstract in this note we prove for instance that the automorphism group of a rational manifold x which is obtained from p k c by a finite sequence of blow ups along smooth centers of dimension at most r with k 2 r 2 has finite image in g l h x z in particular every holomorphic automorphism f x x has zero topological entropy