Rotation number
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Rigidity of critical circle maps Open
We prove that any two $C^4$ critical circle maps with the same irrational\nrotation number and the same odd criticality are conjugate to each other by a\n$C^1$ circle diffeomorphism. The conjugacy is $C^{1+\\alpha}$ for Lebesgue\nalmost ev…
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Quantitative quasiperiodicity Open
The Birkhoff Ergodic Theorem concludes that time averages, i.e., Birkhoff\naverages, $\\Sigma_{n=0}^{N-1} f(x_n)/N$ of a function $f$ along a length $N$\nergodic trajectory $(x_n)$ of a function $T$ converge to the space average\n$\\int f …
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Prime ends rotation numbers and periodic points Open
We study the problem of existence of a periodic point in the boundary of an invariant domain for a surface homeomorphism. In the area-preserving setting, a complete classification is given in terms of rationality of Carathéodory’s prime en…
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Measuring quasiperiodicity Open
The Birkhoff Ergodic Theorem asserts under mild conditions that Birkhoff averages (i.e. time averages computed along a trajectory) converge to the space average. For sufficiently smooth systems, our small modification of numerical Birkhoff…
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Uniform bounds for diffeomorphisms of the torus and a conjecture of Boyland Open
We consider $C^{1+\\epsilon}$ diffeomorphisms of the torus, denoted $f,$\nhomotopic to the identity and whose rotation sets have interior. We give some\nuniform bounds on the displacement of points in the plane under iterates of a\nlift of…
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Analysis on rotation timing of dynamic Rotating latent-energy-storage envelope (RLESE) Open
The application efficiency of the Dynamic Rotating Latent-Energy-Storage Envelope (DRLESE) system is highly contingent upon dynamic rotation timings. To gain the optimal rotation timings, six different timings were examined by employing th…
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Rotation number of contracted rotations Open
International audience
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EFFECT OF ROTATION RATES ON THE LAMINAR FLOW AND HEAT TRANSFER PAST A CIRCULAR CYLINDER Open
In this work, forced convection heat transfer past a rotating circular cylinder with a constant non-dimensional rotation rate α varying from 0 to 6 was investigated for Reynolds numbers of 20-200 and a Prandtl number of 0.7. The numerical …
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High Reynold Number LES of a Rotating Two-Pass Ribbed Duct Open
Cooling of gas turbine blades is critical to long term durability. Accurate prediction of blade metal temperature is a key component in the design of the cooling system. In this design space, spatial distribution of heat transfer coefficie…
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Irrational rotation factors for conservative torus homeomorphisms Open
We provide an equivalent characterization for the existence of one-dimensional irrational rotation factors of conservative torus homeomorphisms that are not eventually annular. It states that an area-preserving non-annular torus homeomorph…
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Local Rigidity of Diophantine Translations in Higher-dimensional Tori Open
We prove a theorem asserting that, given a Diophantine rotation $\\alpha $ in\na torus $\\T ^{d} \\equiv \\R ^{d} / \\Z ^{d}$, any perturbation, small enough in\nthe $C^{\\infty}$ topology, that does not destroy all orbits with rotation\nv…
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Effect of Coriolis and centrifugal forces on flow and heat transfer at high rotation number and high density ratio in non orthogonally internal cooling channel Open
Numerical predictions of three-dimensional flow and heat transfer are performed for a two-pass square channel with 45° staggered ribs in non-orthogonally mode-rotation using the second moment closure model. At Reynolds number of 25,000, th…
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Rotation Number as a Complete Topological Invariant of a Simple Isotopic Class of Rough Transformations of a Circle Open
The problem of the existence of a simple arc connecting two structurally stable systems on a closed manifold is included in the list of the fifty most important problems of dynamical systems.This problem was solved by S. Newhouse and M. Pe…
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Topology of irrationally indifferent attractors Open
We study the post-critical set of a class of holomorphic systems with an irrationally indifferent fixed point. We prove a trichotomy for the topology of the post-critical set based on the arithmetic of the rotation number at the fixed poin…
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Forced rotation enhances cylinder flow-induced vibrations at subcritical Reynolds number Open
When a cylinder is mounted on an elastic support within a current, vortex-induced vibrations (VIV) may occur down to a Reynolds number ( Re ) close to $20$ , based on the body diameter ( $D$ ) and inflow velocity ( $U$ ), i.e. below the cr…
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Dynamic properties of a discrete population model with diffusion Open
We study the dynamical properties of a discrete population model with diffusion. We survey the transcritical, pitchfork, and flip bifurcations of nonhyperbolic fixed points by using the center manifold theorem. For the degenerate fixed poi…
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A 2D piecewise-linear discontinuous map arising in stock market modeling: Two overlapping period-adding bifurcation structures Open
We consider a 2D piecewise-linear discontinuous map defined on three partitions that drives the dynamics
\nof a stock market model. This model is a modification of our previous model associated with a map defined
\non two partitions. In th…
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Periodic measures and partially hyperbolic homoclinic classes Open
International audience
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Renormalization of Bicritical Circle Maps Open
A general ansatz in Renormalization Theory, already established in many\nimportant situations, states that exponential convergence of renormalization\norbits implies that topological conjugacies are actually smooth (when\nrestricted to the…
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Twisting Somersault Open
A complete description of twisting somersaults is given using a reduction to a time-dependent Euler equation for non-rigid body dynamics. The central idea is that after reduction the twisting motion is apparent in a body frame, while the s…
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Classical and quantum rotation numbers of asymmetric-top molecules Open
We study the classical and quantum rotation numbers of the free rotation of\nasymmetric top molecules. We show numerically that the quantum rotation number\nconverges to its classical analog in the semi-classical limit. Different\nasymmetr…
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On mixing diffeomorphisms of the disk Open
We prove that a real analytic pseudo-rotation $f$ of the disc or the sphere is never topologically mixing. When the rotation number of $f$ is of Brjuno type, the latter follows from a KAM theorem of Rüssmann on the stability of real analyt…
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EFFECTS OF ROTATION ON UNSTEADY FLUID FLOW AND FORCED CONVECTION IN THE ROTATING CURVED SQUARE DUCT WITH A SMALL CURVATURE Open
In recent years, the analysis of flow disposition in a curved duct (CD) has greatly attracted researchers because it is broadly used in engineering devices. In the present paper, unsteady flow characteristics of energy transfer (HT) in a r…
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A finite dimensional approach to Bramham’s approximation theorem Open
Using pseudoholomorphic curve techniques from symplectic geometry, Barney Bramham proved recently that every smooth irrational pseudo-rotation of the unit disk is the limit, for the topology, of a sequence of smooth periodic diffeomorph…
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From Pseudo-Rotations to Holomorphic Curves via Quantum Steenrod Squares Open
In the context of symplectic dynamics, pseudo-rotations are Hamiltonian diffeomorphisms with finite and minimal possible number of periodic orbits. These maps are of interest in both dynamics and symplectic topology. We show that a closed,…
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Exploration of Filled-In Julia Sets Arising from Centered Polygonal Lacunary Functions Open
Centered polygonal lacunary functions are a particular type of lacunary function that exhibit properties which set them apart from other lacunary functions. Primarily, centered polygonal lacunary functions have true rotational symmetry. Th…
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Fink type conjecture on affine-periodic solutions and Levinson's conjecture to Newtonian systems Open
This paper concerns the existence of affine-periodic solutions for differential systems (including functional differential equations) and Newtonian systems with friction. This is a kind of pattern solutions in time-space, which may be peri…
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On the dynamics of minimal homeomorphisms of $\mathbb{T}^2$ which are not pseudo-rotations Open
We prove that any minimal $2$-torus homeomorphism which is isotopic to the identity and whose rotation set is not just a point exhibits uniformly bounded rotational deviations on the perpendicular direction to the rotation set. As a conseq…
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Effect of Rotation and Hole Arrangement in Cold Bridge-Type Impingement Cooling Systems Open
Experimental activity has been performed to study different impingement cooling schemes in static and rotating conditions. Geometry replicates a leading-edge cold bridge system, including a radial supply channel and five rows of film-cooli…
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Differentiable Rigidity for quasiperiodic cocycles in compact Lie groups Open
We study close-to-constants quasiperiodic cocycles in $\\mathbb{T} ^{d} \\times\nG$, where $d \\in \\mathbb{N} ^{*} $ and $G$ is a compact Lie group, under the\nassumption that the rotation in the basis satisfies a Diophantine condition. W…