인공고관절의 세라믹 볼 헤드의 기계적 안정성 평가를 위한 3 차원 유한요소 해석

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Introduction to the Modern Theory of Dynamical Systems

Part I. Examples and Fundamental Concepts Introduction 1. First examples 2. Equivalence, classification, and invariants 3. Principle classes of asymptotic invariants 4. Statistical behavior of the orbits and introduction to ergodic theory 5. Smooth invariant measures and more examples Part II. Local Analysis and Orbit Growth 6. Local hyperbolic theory and its applications 7. Transversality and genericity 8. Orbit growth arising from topology 9. Variational aspects of dynamics Part III. Low-Dimensional Phenomena 10. Introduction: What is low dimensional dynamics 11. Homeomorphisms of the circle 12. Circle diffeomorphisms 13. Twist maps 14. Flows on surfaces and related dynamical systems 15. Continuous maps of the interval 16. Smooth maps of the interval Part IV. Hyperbolic Dynamical Systems 17. Survey of examples 18. Topological properties of hyperbolic sets 19. Metric structure of hyperbolic sets 20. Equilibrium states and smooth invariant measures Part V. Sopplement and Appendix 21. Dynamical systems with nonuniformly hyperbolic behavior Anatole Katok and Leonardo Mendoza.

Introduction to the Modern Theory of Dynamical Systems: EQUILIBRIUM STATES AND SMOOTH INVARIANT MEASURES

Introduction to the Modern Theory of Dynamical Systems: INTRODUCTION: WHAT IS LOW-DIMENSIONAL DYNAMICS?

1. Elementary Celestial and Hamiltonian Mechanics 2. Quasi-Integrable Hamiltonian System 3. Kam Tori 4. Single Resonance Dyanmics 5. Numerical Tools for the Detection of Chaos 6. Interactions Among Resonances 7. Secular Dynamics of the Planets 8. Secular Dynamics of Small Bodies 9. Mean Motion Resonances 10. Three Body Resonances 11. Secular Dynamics Inside Mean Motion Resonances 12. Global Dynamical Structure of the Belts of Small Bodies.

Modern celestial mechanics : aspects of solar system dynamics

We introduce a geometric mechanism for di?usion in a priori unstable
nearly integrable dynamical systems. It is based on the observation that
resonances, besides destroying the primary KAM tori, create secondary tori
and tori of lower dimension. We argue that these objects created by resonances
can be incorporated in transition chains taking the place of the
destroyed primary KAM tori.
We establish rigorously the existence of this mechanism in a simple
model that has been studied before. The main technique is to develop a
toolkit to study, in a unified way, tori of different topologies and their invariant
manifolds, their intersections as well as shadowing properties of these
bi-asymptotic orbits. This toolkit is based on extending and unifying standard
techniques. A new tool used here is the scattering map of normally
hyperbolic invariant manifolds.
The model considered is a one-parameter family, which for " = 0 is an
integrable system. We give a small number of explicit conditions the jet of
order 3 of the family that, if verified imply diffusion. The conditions are
just that some explicitely constructed functionals do not vanish identically
or have non-degenerate critical points, etc.
An attractive feature of the mechanism is that the transition chains are
shorter in the places where the heuristic intuition and numerical experimentation
suggests that the diffusion is strongest.

A Geometric Mechanism for Diffusion in Hamiltonian Systems Overcoming the Large Gap Problem: Heuristics And Rigorous Verification on a Model

Geometric properties of the scattering map of a normally hyperbolic invariant manifold

We give a proof based in geometric perturbation theory of a result proved by J. N. Mather using variational methods. Namely, the existence of orbits with unbounded energy in perturbations of a generic geodesic flow in ?2 by a generic periodic potential.

A Geometric Approach to the Existence of Orbits with Unbounded Energy in Generic Periodic Perturbations by a Potential of Generic Geodesic Flows of ? 2}

We consider fast quasiperiodic perturbations with two frequencies (1/ɛ,γ/$epsiv;) of a pendulum, where γ is the golden mean number. The complete system has a two-dimensional invariant torus in a neighbourhood of the saddle point. We study the splitting of the three-dimensional invariant manifolds associated to this torus. Provided that the perturbation amplitude is small enough with respect to ɛ, and some of its Fourier coefficients (the ones associated to Fibonacci numbers), are separated from zero, it is proved that the invariant manifolds split and that the value of the splitting, which turns out to be exponentially small with respect to ɛ, is correctly predicted by the Melnikov function.

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Exponentially Small Splitting of Separatrices Under Fast Quasiperiodic Forcing

We consider perturbations of integrable, area preserving nontwist maps of the annulus (those are maps in which the twist condition changes sign). These maps appear in a variety of applications, notably transport in atmospheric Rossby waves. We show in suitable two-parameter families the persistence of critical circles (invariant circles whose rotation number is the maximum of all the rotation numbers of points in the map) with Diophantine rotation number. The parameter values with critical circles of frequency $\omega_0$ lie on a one-dimensional analytic curve.Furthermore, we show a partial justification of Greene's criterion: If analytic critical curves with Diophantine rotation number $\omega_0$ exist, the residue of periodic orbits (that is, one fourth of the trace of the derivative of the return map minus 2) with rotation number converging to $\omega_0$ converges to zero exponentially fast. We also show that if analytic curves exist, there should be periodic orbits approximating them and indicate how ...

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Amadeu Delshams

Papers

A Geometric Mechanism for Diffusion in Hamiltonian Systems Overcoming the Large Gap Problem: Heuristics And Rigorous Verification on a Model

Geometric properties of the scattering map of a normally hyperbolic invariant manifold

A Geometric Approach to the Existence of Orbits with Unbounded Energy in Generic Periodic Perturbations by a Potential of Generic Geodesic Flows of ? 2}

Exponentially Small Splitting of Separatrices Under Fast Quasiperiodic Forcing

KAM theory and a partial justification of Greene's criterion for nontwist maps