A diffeomorphism f has a heterodimensional cycle if it displays two (transitive) hyperbolic sets K and K' with different indices such that the unstable set of K intersects the stable one of K' and vice versa. We prove that it is possible to find robust heterodimensional cycles for families of polynomial automorphisms of C^3 . The proof is based on Bonatti-D{í}az blenders.
El objetivo de esta investigación consiste en reconocer la especificidad de la actividad artística, sus preocupaciones, problemas y soluciones. Se introduce el concepto de “idea artística” para designar la resolución de un problema estético, idea sensible, que plantea el soporte material mismo (pintura, notas y mármol) y que no puede, contrariamente a las ideas intelectuales (filosóficas, sociológicas, etc.), traducirse en palabras o ser formulada de otra manera. Las ideas del arte son el verdadero significado de las obras, las cuales no son traducciones o expresiones de otras ideas no artísticas, como lo sostiene una cierta crítica hermenéutica. Son dichas ideas las que provocan una emoción especial, específicamente estética, y que el juicio estético pretende evaluar.
Abstract National Institute of Rock Mechanics, Bangalore, India is actively involved in conducting in-situ stress measurements for numerous projects both in India and its neighboring countries for the last 30 years. The stress measurements were conducted at various hydroelectric project sites of Himalayan areas at a depth of 350 m from the surface and recently in-situ stress measurements were carried out at a depth of 600 m from the surface at one of the proposed mining blocks of Singareni Collieries Company Limited which is first time in India. With the available data on in-situ stress measurements, the Stress Map of India has been prepared. This is a significant contribution towards design and development of World Stress Map. These stress orientation directions are advantageously useful not only for academic study and research but also for gathering the enormous information on a global perspective to comprehend the geodynamics and plate movement.
We discuss some ergodic properties of the generalized Gauss transformation $$T_N(x)=\{\frac{N}{x}\}.$$ We generalize a series of results for the regular continued fractions, such as Khinchin's constant and Lévy's constant.
The Tribonacci sequence $\mathbb{T}$ is the fixed point of the substitution $σ(a,b,c)=(ab,ac,a)$. In this note, we give the explicit expressions of the numbers of distinct squares and cubes in $\mathbb{T}[1,n]$ (the prefix of $\mathbb{T}$ of length $n$).
In this paper, we study infinite-dimensional Lagrangian systems where the potential functions are periodic, rearrangement invariant and weakly upper semicontinuous. And we prove that there exists a calibrated curve for every $M\in L^{2}(I)$.
We consider a family of homoclinic groups and Gordin's type invariants of measure-preserving actions, state their connections with factors, full groups, ranks, rigidity, multiple mixing and realize such invariants in the class of Gaussian and Poisson suspensions.
We establish sufficient conditions for the upper semicontinuity and the continuity of the entropy of Sinai probability measures invariant by partially hyperbolic diffeomorphisms and discuss their application in several examples.
By application of KAM theorem to Lidov-Ziglin's global study of the quadrupolar approximation of the spatial lunar three-body problem, we establish the existence of several families of quasi-periodic orbits in the spatial lunar three-body problem.
We consider the dynamics of holomorphic polynomials in $\mathbb C$. We show that the ergodic properties of the map can be seen already from the real parts of the orbits.
Let $M$ be a compact real analytic manifold of finite dimension. There is a function $a: (0,+\infty)\to [0,+\infty)$ with $\lim_{t\to0}a(t)=0$ such that, the tail entropy $h^{*}(f,\varepsilon)$ of any real analytic map $f$ on $M$ is uniformly bounded above by the scale $a(\varepsilon)$.
Certain dynamical models of competition have a unique invariant hypersurface to whichevery nonzero tractory is asymptotic, having simple geometry and topology.
In this paper we investigate the perturbation properties of rational Misiurewicz maps, when the Julia set is the whole sphere (the other case is treated in [1]). In particular, we show that if f is a Misiurewicz map and not a flexible Lattes map, then we can find a hyperbolic map arbitrarily close to f.
We prove that multiple-recurrence and polynomial-recurrence of invertible infinite measure preserving transformations are both properties which pass to extensions.
We study the notion of Fagnano orbits for dual polygonal billiards. We used them to characterize regular polygons and we study the iteration of the developing map.
We study the action of the horocycle flow on the moduli space of abelian differentials in genus two. In particular, we exhibit a classification of a specific class of probability measures that are invariant and ergodic under the horocycle flow on the stratum H(1,1).
Fibered holomorphic dynamics are skew-product transformations over an irrational rotation, whose fibers are holomorphic functions. In this paper we study such a dynamics on a neighborhood of an invariant curve. We obtain some results analogous to the results in the non fibered case.
In this paper we prove that if two self-similar tiling systems, with respective stretching factors $λ_1$ and $λ_2$, have a common factor which is a non periodic tiling system, then $λ_1$ and $λ_2$ are multiplicatively dependent.