Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuous Transitive Maps on the Interval Revisited   In this note, continuous transitive maps $f$ on the interval $I$ are
re-addressed, where $I$ denotes one of the intervals: $(-\infty, \infty)$,
$(-\infty, a]$, $[b, \infty)$, $[a, b]$, where $a < b$ are real numbers. Such
maps must have a fixed point, say $z$, in the interior of $I$. Some well-known
properties of such maps are re-proved in a systematic way according to the
following :
  (1) $f$ moves some point $c \ne z$ away from $z$, i.e., fo some point $c \ne
z$, we have $f(c) \le c < z$ or $z < c \le f(c)$;
  (2) $f$ moves some point $\hat c \ne z$ towards but not "over" $z$, i.e., for
some point $\hat c \ne z$, we have $\hat c < f(\hat c) < z$ or $z < f(\hat c) <
\hat c$; and
  (3) $f$ moves all points $x \ne z$ to the other side of $z$, i.e., for all
points $x \ne z$, we have $x < z \le f(x)$ and $f(x) \le x < z$.
  The proofs are arranged in such ways that they yield the same results. For
example, Theorem 3 treats maps satisfying Condition (1) or Condition (2) while
Theorem 4 treats separately maps satisfying Condition (1) and, Conditions (2)
or (3). Characterizations of continuous bitransitive maps on an interval are
re-addressed and a new chaotic property of continuous bitransitive maps is also
introduced (Theorem 8, p.21).
  In this revision, we correct Corollary 9 and some errors in the proof of
Theorem 8 and move the Appendix to a different paper [15] in which we
generalize Theorem 8 for continuous weakly mixing (i.e., bitransitive) maps on
intervals to continuous weakly mixing maps and continuous mixing maps on
infinite separable locally compact metric spaces.

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The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci