A C 1-generic dichotomy for diﬀeomorphisms: Weak forms of hyperbolicity or inﬁnitely many sinks or sources
By C. Bonatti, L. J. D´ ıaz, and E. R. Pujals*
A Ricardo Ma˜e (1948–1995), por todo su trabajo n´ Abstract We show that, for every compact n-dimensional manifold, n ≥ 1, there is a residual subset of Diﬀ1 (M ) of diﬀeomorphisms for which the homoclinic class of any periodic saddle of f veriﬁes one of the following two possibilities: Either it is contained in the closure of an inﬁnite set of sinks or sources (Newhouse phenomenon), or it presents some weak form of...
Scientists who dedicate their research activity to biomaterials pass through the typical
dichotomy that often characterizes the basic research.
On one side is the wish of exploring new frontiers of chemistry, physics, biology,
medicine, pharmaceutics and all other disciplines to which biomaterials can be
applied. Constantly improving of scientific knowledge would feed the freedom of
attempting new strategies for producing materials with always tailored and improved
Scientists who dedicate their research activity to biomaterials pass through the typical
dichotomy that often characterizes the basic researc. On one side is the wish of
exploring new frontiers of chemistry, physics, biology, medicine, pharmaceutics and
all other disciplines to which biomaterials can be applied. The constantly improving
scientific knowledge would feed the freedom of attempting new strategies for
producing materials with always tailored and improved characteristics.
Few things in the universe are constant over thousands or millions of
years, not the orbit of the Earth around the sun, the height of eroding
mountains, the distribution of boreal forests, or the abundance of a
particular species. As we shift our attention from the stellar and global to
the regional and local, then the more likely it is that we will encounter
things that change over even short spans of time.
What is the nature of Nature? Is it harmonious and graceful? Is it divine and
providential? Is it cruel and wild? These days, answers to the question 'What is the
nature of Nature?' often reverberate with claims of natural unity: every living thing in
nature, and this includes humanity, is united.
The unity of nature idea appears in many different forms; in the speeches of
environmentally conscious politicians, in the academic writings of scientists, in the
sermons of theological leaders, and in the slogans of social activists.
With the ending of the political dichotomy in world politics around 1990, the
good governance principle came to occupy an important position in judgements
about political regimes in developing countries. Good governance became an
important objective in the policies of many aid-giving Western countries and the
main international financial institutions, such as the World Bank. Increasingly,
however, good governance and market-oriented economic reform came to be
subsumed under one heading, leading to what has been called a post-Washington
Finding a solution to structural poverty requires a review of the devel-
opment model as well as the macroeconomic policies adopted by gov-
ernments. Social development and economic growth must be under-
stood as integral parts of the same process. Eliminating the causes of
structural poverty requires overcoming the false dichotomy between the
social and economic aspects of development. In other words, poverty
reduction should be the main objective of macroeconomic policies in
the social sectors....
The Dichotomy of Inpatient and Outpatient Internal Medicine The hospital environment has transformed dramatically over the past few decades. In more recent times, emergency departments and critical care units have evolved to identify and manage critically ill patients, allowing them to survive formerly fatal diseases. There is increasing pressure to reduce the length of stay in the hospital and to manage complex disorders in the outpatient setting.
Administrative law is an exciting topic, in particular for those with an interest
in how the law seeks to control the exercise of the enormous powers of the
modern state. In the development of the law generally, modern administrative
law is a recent, very largely post-Second World War, phenomenon. In legal education,
it has grown over the past 20 years from being a component within
established constitutional law courses to being a subject in its own right. Its
relationship with constitutional law, however, must not be forgotten....
The best way to ensure that infants are not born with HIV or acquire
it during breast-feeding is to provide HIV-positive women the care they
need for their own HIV disease. Vertical transmission is certainly an issue
where the false dichotomy pitting prevention and treatment against
each other is truly nonsense—in studies where HIV-positive women
get appropriate care, HIV transmission to infants is largely eradicated2
Vertical transmission programs must be linked with HIV treatment
Doctors are obviously not undiscerning recipients of advertising and other forms of promotion. Smith (2003) says “Your opinion may not be bought, but it seems rude to say critical things about people who have hosted you so well.” He goes on to say that the easy dichotomy of pharmaceutical giants as villains and doctors as innocent victims is over-simplifying the situation. Clearly doctors need to use drugs in order to deliver their services, and it is also reasonable that firms should be allowed to promote their products.
The second, developed through narcissism and the constitution of the
ego, comes from identification with the image seen. Thus, in film terms, one implies
a separation of the erotic identity of the subject from the object on the screen (active
scopophilia), the other demands identification of the ego with the object on the
screen through the spectator's fascination with and recognition of his like. The first is
a function of the sexual instincts, the second of ego libido. This dichotomy was
crucial for Freud.
Though there exists a body of feminist film making in Hindi cinema, the leading lady of Hindi films has more or
less played defined roles which conform to the values upheld by Indian society. Women in Bollywood have been
uni-dimensional characters, who are good or bad, white or black. There are no shades of grey. This dichotomy
was reinforced in popular films which distinguished between the heroine and the vamp, the wife and the other
woman. Films have also been inspired to a large extent from religion and mythology whereby women characters
were seen as the epitome of virtue and...
Another trend to be examined in the depiction of female characters is the clear dichotomy which is followed.
The woman is docile, domestic, honourable, noble, and ideal or she is the other extreme – wayward, reckless
and irresponsible. Why does Bollywood shy away from taking the middle path? Where are women who are good
or bad as per the situation they face in their lives? Where are the women who negotiate with troubles on a daily
basis and emerge victorious? In David Dhawan‟s Biwi no.1 (1999), the wife played by Karishma Kapoor is
shown to have sacrificed...
We show that the integrated Lyapunov exponents of C 1 volume-preserving diﬀeomorphisms are simultaneously continuous at a given diﬀeomorphism only if the corresponding Oseledets splitting is trivial (all Lyapunov exponents are equal to zero) or else dominated (uniform hyperbolicity in the projective bundle) almost everywhere. We deduce a sharp dichotomy for generic volume-preserving diﬀeomorphisms on any compact manifold:
ver fifty years ago, Vannevar Bush released his enormously influential report, Science, the Endless Frontier, which asserted a dichotomy between basic and applied science. This view was at the core of the compact between government and science that led to the golden age of scientific research after World War II--a compact that is currently under severe stress. In this book, Donald Stokes challenges Bush's view and maintains that we can only rebuild the relationship between government and the scientific community when we understand what is wrong with that view.
Others want no structure. They like to let the future unfold as
it will and to creatively adapt to its conditions. They feel that struc-
ture gets in the way of creativity and it is unrealistic to tie themselves
This division between the structured and unstructured schools of
thought is one of many such dichotomies. The knee-jerk reaction to
dichotomy is conflict; however, in the wisdom way, we apply the prin-
ciple of balance, that dynamic state of ease that occurs when all oppos-
ing forces are present to the right degree. There is nothing in excess and
LEGAL CULTURE VERSUS Legal Tradition? The dichotomy is
unreal in most circumstances. But not in all.
Legal culture is legal tradition, and legal tradition is legal culture. But with
an exception. Those living the culture, namely lawyers including judges and
law professors, are usually unaware of the tradition. They are often unaware
of, and indifferent to, history. (I would like readers to know that I am dealing
only with private law. Constitutional law is beyond my expertise).