scholarly journals A new method for measuring the splitting of invariant manifolds

Equadiff 99 ◽  
2000 ◽  
pp. 961-966 ◽  
Author(s):  
David Sauzin
Keyword(s):  
Invariant Manifolds ◽  
New Method ◽  
Splitting Of Invariant Manifolds

scholarly journals Exponentially Small Lower Bounds for the Splitting of Separatrices to Whiskered Tori with Frequencies of Constant Type

2014 ◽  
Vol 24 (08) ◽  
pp. 1440011 ◽  
Author(s):  
Amadeu Delshams ◽  
Marina Gonchenko ◽  
Pere Gutiérrez
Keyword(s):  
Lower Bounds ◽  
Invariant Manifolds ◽  
Irrational Number ◽  
Melnikov Method ◽  
Arithmetic Properties ◽  
Constant Type ◽  
Whiskered Tori ◽  
Vector Formula ◽  
Splitting Of Invariant Manifolds ◽  
Exponentially Small

We study the splitting of invariant manifolds of whiskered tori with two frequencies in nearly-integrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We consider a two-dimensional torus with a fast frequency vector [Formula: see text], with ω = (1, Ω) where Ω is an irrational number of constant type, i.e. a number whose continued fraction has bounded entries. Applying the Poincaré–Melnikov method, we find exponentially small lower bounds for the maximal splitting distance between the stable and unstable invariant manifolds associated to the invariant torus, and we show that these bounds depend strongly on the arithmetic properties of the frequencies.

Selective Sampling and Orientation of Non-Homogeneous Tissues

1968 ◽  
Vol 26 ◽  
pp. 98-99
Author(s):  
C. C. Clawson ◽  
L. W. Anderson ◽  
R. A. Good
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
Light Microscopy ◽  
Random Sampling ◽  
New Method ◽  
Microscope Examination ◽  
Small Areas ◽  
Selective Sampling ◽  
Large Numbers ◽  
Specific Orientation

Investigations which require electron microscope examination of a few specific areas of non-homogeneous tissues make random sampling of small blocks an inefficient and unrewarding procedure. Therefore, several investigators have devised methods which allow obtaining sample blocks for electron microscopy from region of tissue previously identified by light microscopy of present here techniques which make possible: 1) sampling tissue for electron microscopy from selected areas previously identified by light microscopy of relatively large pieces of tissue; 2) dehydration and embedding large numbers of individually identified blocks while keeping each one separate; 3) a new method of maintaining specific orientation of blocks during embedding; 4) special light microscopic staining or fluorescent procedures and electron microscopy on immediately adjacent small areas of tissue.

A new method for the determination of nitrates

1960 ◽  
Vol 23 ◽  
pp. 227-232 ◽  
Author(s):  
P WEST ◽  
G LYLES
Keyword(s):  
New Method
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